4 The H-C = 6 index related to Sandra CarilloÕs scientific production (H-C> 5)

For each one of the collected citations or the ISI or the Scopus code are indicated. Sometimes also the MathSciNet code appears.

In this Section it is shown that the H-C is greater than 5. To achieve thos result, the citations referring to the following papers are considered:

4.1  H-C=10    WOS:268614500029,  2-s2.0-68749111018
S. Carillo, C. Schiebold, Noncommutative Korteweg-de Vries and modified Korteweg-de Vries hierarchies via recursion methods. J. Math. Phys. 50 (2009), no. 7, 073510, 14 pp.

4.2  H-C=7     WOS:000223426000008, 2-s2.0-4444342069
Amendola G. e Carillo S., Thermal work and minimum free energy in a heat conductor with memory, Quarterly Journal Mech. Appl. Math., 57 3, (2004), 429-446; doi: 10.1093∕qjmam∕57.3.429;

4.3  H-C=6    WOS:000291106000032, 2-s2.0-79957899011
S. Carillo, C. Schiebold, Matrix Korteweg- de Vries and modified Korteweg-de Vries hierarchies. Noncommutative Soliton Solutions,   J. Math. Phys., 52, 5 (2011), 053507, publ. online 13 May 2011;

4.4  H-C=6    WOS:000297524200002, 2-s2.0-81155130526
S. Carillo, Existence, uniqueness and exponential decay: An evolution problem in heat conduction with memory,   Quarterly of Applied Mathematics, 69, 4 (2011), 635-649;

4.5  H-C=8    WOS:000302022500003, 2-s2.0-84858822229
S. Carillo, C. Schiebold. On the recursion operator for the noncommutative Burgers hierarchy. J. Nonlinear Math. Phys. 19 (2012), no. 1, 1250003, 11 pp.;
4.6  H-C=6      WOS: 000071726200009,  2-s2.0-0039394289
Oevel W., Carillo S., Squared Eigenfunction Symmetries for Soliton Equations: Part I,  J. Math. Anal. and Appl., 217, (1998), 161-178; doi:10.1006/jmaa.1997.5707
4.7 H-C=6      2-s2.0-0008859965
A Quattropani, F , S Carillo, Two-photon transitions to excited states in atomic hydrogen, Physical Review A 25 (6), 3079;
4.8 H-C=6    WOS: A1987L230300001,  2-s2.0-0001019623  (only with secondary items too)
Rogers C., Carillo S.,  On reciprocal properties of the Caudrey-Dodd-Gibbon and Kaup-Kupershmidt hierarchies,  Physica Scripta, 36, (1987), 865-869,  doi:10.1088/0031-8949/36/6/001
4.9  H-C=4     WOS:71726200010,  2-s2.0-0040577087
Oevel W., Carillo S.,  Squared Eigenfunction Symmetries for Soliton Equations: Part II,  J. Math. Anal. and Appl., 217, (1998), 179-199; doi:10.1006/jmaa.1997.5708

4.10  H-C=5    WOS:A1989AC84300027, 2-s2.0-0001759082
Carillo S., Fuchssteiner B.,  The abundant symmetry structure of non linear equations obtained by reciprocal links,  J. Math. Phys., 30, (1989), pp.1606-1613, doi:10.1063/1.528604
A.M.S. 58G35  35Q20  58F07  58G37

Hence, there are 8 papers whose H-C is greater than 5. In the following subsections all the citing papers are listed. The following subsections are devoted to the complete list of publications wherein references to each one of the mentioned articles appear.

4.1 Citations of Carillo S., C. Schiebold Noncommutative Kortewegde Vries and modified Kortewegde Vries Hierarchies via Recursion Methods ,  J. Math. Phys., 50,(2009), 073510, published online 20 July 2009; doi:10.1063/1.3155080

The paper has been cited 9(+2) times: the result is obtained considering all possible sources. I did check that the paper is cited in each one of the articles listed here below. Note that the number of citations is higher than that one in each of the Databases I used (MathSciNet, Scopus, Web of Science and, occasionally, ZentralBlatt Math) further to look on the web, in general. 

H-C=10  since (4x10)/4=10

As a consequence of retrieving also those citations non listed on the databases, but available online, it follows

              Citing Papers


  1.  WOS:000297938300023, 2-s2.0-8285516963        C. Schiebold, Structural properties of the noncommutative KdV recursion operator, J. Math. Phys. 52, 113504 (2011)                                      
  2. WOS:000295165900011, 2-s2.0-80053271619         Jingsong He Junyi Tu, Xiaodong Li and Lihong Wang, Explicit flow equations and recursion operator of the ncKP hierarchy, Nonlinearity 24 2875 doi:10.1088/0951-7715/24/10/011
  3. WOS:000291106000032, 2-s2.0-79957899011        S Carillo, C. Schiebold, Matrix Korteweg-de Vries and modified Korteweg-de Vries hierarchies: Noncommutative soliton solutions J. Math. Phys. 52, 053507 (2011) (controlla codice WOS!!)
  4. WOS:000296923400005, 2-s2.0-80955141251           A L Sakhnovich, The time-dependent Schršdinger equation of dimension k+ 1: explicit and rational solutions via GBDT and multinodes Journal of Physics A Mathematical and Theoretical 44, 475201 (2011)
  5. WOS:000283300100031, 2-s2.0-78649641881          C. Schiebold, The noncommutative AKNS system: projection to matrix systems, countable superposition and soliton-like solutions, Journal of Physics A Mathematical and Theoretical 43, 434030 (2010)
  6. WOS:000304578500001, 2-s2.0-84859416473     M. Irfan, Lax pair representation and Darboux transformation of noncommutative PainlevŽÕs second equation. J. Geom. Phys. 62 (2012), no. 7, 1575Ð1582. 
  7. WOS:000302022500003, 2-s2.0-84858822229       S. Carillo, C. Schiebold. On the recursion operator for the noncommutative Burgers hierarchy. J. Nonlinear Math. Phys. 19 (2012), no. 1, 1250003, 11 pp.
  8. WOS:000295165900011, 2-s2.0-80053271619       J. He, J. Tu,X. Li, L. Wang. Explicit flow equations and recursion operator of the ncKP hierarchy. Nonlinearity 24 (2011), no. 10, 2875Ð2890. 
  9. WOS:000278434100013, 2-s2.0-77953138087      C. Schiebold. Cauchy-type determinants and integrable systems. Linear Algebra Appl. 433 (2010), no. 2, 447Ð475.
  10. WOS:000275974500016.      Carillo Sandra ; Schiebold, Cornelia . A non-commutative operator-hierarchy of Burgers equations and BŠcklund transformations. Applied and industrial mathematics in Italy III, 175Ð185, Ser. Adv. Math. Appl. Sci., 82, World Sci. Publ., Hackensack, NJ, 2010. 
  11. MR2762002 Carillo S. ; Schiebold, C. Recursion techniques and explicit solutions of integrable noncommutative hierarchies. Proceedings ÓWASCOM 2009Ó 15th Conference on Waves and Stability in Continuous Media, 74Ð80, World Sci. Publ., Hackensack, NJ, 2010.

4.2 Citations of Amendola G. e Carillo S., Thermal work and minimum free energy in a heat conductor with memory, Quarterly Journal Mech. Appl. Math., 57 3, (2004), 429-446

The citations received by this paper are 15, hence

H-C=7  since (4x14)/9 =6.22

(Note: one of the citations does not have nor ISI nor Scopus code) (4x14)/9=6,22 hence, even without it, the H-C=7)

The complete list of the references I found (and checked looking at the references therein) is in the following.

Note that none of the databases comprises all the citations. Notably, citations are missing for many different reasons in each one of the Databases. Indeed, for instance, a paper, reviewed in MathSciNet, contains this paper in the Reference list; however, it is not indicated in the citations the same MathSciNet database.

              Citing Papers

  1. WOS:000297524200010, 2-s2.0-81155133396  
    Amendola, Giovambattista ; Fabrizio, Mauro ; Golden, Murrough . Thermodynamics of a non-simple heat conductor with memory. Quart. Appl. Math. 69 (2011), no. 4, 787Ð806.           
  2. WOS:000297524200002, 2-s2.0-81155130526    Carillo, Sandra . Existence, uniqueness and exponential decay: an evolution problem in heat conduction with memory. Quart. Appl. Math. 69 (2011), no. 4, 635Ð649. 
  3. WOS:290406800007, 2-s2.0-79956134379      Carillo, Sandra . An evolution problem in materials with fading memory: solutionÕs existence and uniqueness. Complex Var. Elliptic Equ. 56 (2011), no. 5, 481Ð492  
  4.   WOS:000280382700001, 2-s2.0-77957808367      Amendola, Giovambattista ; Fabrizio, Mauro ; Golden, John Murrough . Minimum free energy in the frequency domain for a heat conductor with memory. Discrete Contin. Dyn. Syst. Ser. B 14 (2010), no. 3, 793Ð816.   
  5. WOS:000277821800008,   2-s2.0-84859558695   Carillo, Sandra . Materials with memory: free energies & solution exponential decay. Commun. Pure Appl. Anal. 9 (2010), no. 5, 1235Ð1248.
  6. WOS:000208720400007       Berti, V. ; Fabrizio, M. ; Giorgi, C. On a doubly nonlinear phase-field model for first-order transitions with memory. Differential Integral Equations 21 (2008), no. 3-4, 325Ð350.
  7. WOS:000254815700001, 2-s2.0-41149130115   Fabrizio, M. ; Giorgi, C. ; Morro, A. A continuum theory for first-order phase transitions based on the balance of structure order. Math. Methods Appl. Sci. 31 (2008), no. 6, 627Ð653.
  8. WOS:000238419200003, 2-s2.0-33748574273      Bonetti, Elena ; Colli, Pierluigi ; Fabrizio, Mauro ; Gilardi, Gianni . Modelling and long-time behaviour for phase transitions with entropy balance and thermal memory conductivity. Discrete Contin. Dyn. Syst. Ser. B 6 (2006), no. 5, 1001Ð1026 (electronic).
  9. WOS:000226501000016,  2-s2.0-30444443795  Carillo, Sandra . Some remarks on materials with memory: heat conduction and viscoelasticity. J. Nonlinear Math. Phys. 12 (2005), suppl. 1, 163Ð178. 
  10. WOS:000249432700003, 2-s2.0-34547146397        Golden, J.M. A proposal concerning the physical rate of dissipation of materials with memory: The non-isothermal case (2007) Mathematics and Mechanics of Solids, 12 (4), pp. 403-449.
  11. 2-s2.0-84859555221,   Amendola, Giovambattista ; Manes, Adele . Minimum free energy for a rigid heat conductor and application to a discrete spectrum model. Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 10 (2007), no. 3, bis, 969Ð987. 
  12. 2-s2.0-74549138567,       Amendola, G., Fabrizio, M., Franchi, F. On the minimum free energy for a rigid heat conductor with memory effects (2009) Nonlinear Dynamics and Systems Theory, 9 (4), pp. 333-360.  
  13. 2-s2.0-34547517975,        Amendola, G., Bosello, C.A., Fabrizio, M. Maximum recoverable work and pseudofree energies for a rigid heat conductor (2007) Nonlinear Oscillations, 10 (1), pp. 4-21. 
  14. 2-s2.0-84859555221    Amendola, Giovambattista ; Carillo, Sandra ; Manes, Adele . Classical free energies of a heat conductor with memory and the minimum free energy for its discrete spectrum model. Boll. Unione Mat. Ital. (9) 3 (2010), no. 3, 421Ð446.
  15.  Caucci, A. M. Minimal representations, controllability and free energies in a heat conductor with memory. Nonlinear Dyn. Syst. Theory 6 (2006), no. 2, 111Ð127.

4.3 Citations of S. Carillo, C. Schiebold Matrix Korteweg- de Vries and modified Korteweg-de Vries hierarchies. Noncommutative Soliton Solutions,   J. Math. Phys., 52, 5 (2011), 053507, 21pp. publ. online 13 May 2011;

This article has been cited 3 times, and hence, the related index is:

H-C=6  since (4x3)/2=6

              Citing Papers

  1. WOS:302022500003,  2-s2.0-84858822229       Carillo S., C. Schiebold On the recursion operator for the noncommutative Burgers hierarchy,   J. Nonlinear Math. Phys., 19 n.ro 1 (2012);   
  2.  WOS:000297938300023, 2-s2.0-8285516963          C Schiebold, Structural properties of the noncommutative KdV recursion operator Journal of Mathematical Physics, 52, 113504,  2011;       
  3. WOS:000310951700009, 2-s2.0-84861463130        Carillo S., Nonlinear Evolution Equations: BŠcklund Transformations and BŠcklund Charts, Acta Applicandae Mathematicae, 122, n.ro 1, pp. 93-106, (2012); doi: 10.1007/s10440-012-9729-8; 

4.4 Citations of S. Carillo,  Existence, uniqueness and exponential decay: An evolution problem in heat conduction with memory,   Quarterly of Applied Mathematics, 69, 4 (2011), 635-649;

This article has been cited 3 times, and hence, the related index is:

H-C=6  since (4x3)/2=6

Citing Papers             

  1. WOS:290406800007, 2-s2.0-79956134379     Carillo, Sandra . An evolution problem in materials with fading memory: solutionÕs existence and uniqueness. Complex Var. Elliptic Equ. 56 (2011), no. 5, 481Ð492.   

  2. WOS:000307087500007        Carillo Sandra . Nonlinear hyperbolic equations and linear heat conduction with memory. Mechanics of microstructured solids. 2, 63Ð70, Lect. Notes Appl. Comput. Mech., 50, Springer, Berlin, 2010. ;       
  3. WOS:000277821800008,  2-s2.0-84859558695        S. Carillo, Materials with Memory: Free Energies & SolutionsÕ Exponential Decay, Communications on Pure And Applied Analysis, p. 1235 Ð 1248, ISSN: 1534-0392, Volume 9, Number 5, September (2010); 

4.5 Citations of    WOS:000302022500003, 2-s2.0-84858822229

S. Carillo, C. Schiebold. On the recursion operator for the noncommutative Burgers hierarchy. J. Nonlinear Math. Phys. 19 (2012), no. 1, 1250003, 11 pp.;

H-C=8  since (4x2)/1=8

              Citing Papers


  1. WOS:000275974500016.      Carillo Sandra ; Schiebold, Cornelia . A non-commutative operator-hierarchy of Burgers equations and BŠcklund transformations. Applied and industrial mathematics in Italy III, 175Ð185, Ser. Adv. Math. Appl. Sci., 82, World Sci. Publ., Hackensack, NJ, 2010. 
  2.  WOS:000310951700009, 2-s2.0-84861463130        Carillo S., Nonlinear Evolution Equations: BŠcklund Transformations and BŠcklund Charts, Acta Applicandae Mathematicae, 122, n.ro 1, pp. 93-106, (2012); doi: 10.1007/s10440-012-9729-8.                                  

4.6 Citations of Oevel W., Carillo S.  Squared Eigenfunction Symmetries for Soliton Equations: Part I,  J. Math. Anal. and Appl., 217, (1998), 161Ð178; doi:10.1006/jmaa.1997.5707

The paper has been cited 19 times: the result is obtained considering all possible sources. I did check that the paper appears in all the papers listed here below. Hence,

H-C=6  since (4x19)/15=5.1


Note that the number of citations is much closer to than that one obtained from the Databases I used (MathSciNet, Scopus and Web of Science) since this article was published in 1998.

This papers appears also in the reference list of the following preprint (not included in my H-C computation):
Ghost symmetry of the discrete KP hierarchy C Li, J Cheng, K Tian, M Li, J He - arXiv preprint arXiv:1201.4419, 2012 - arxiv.org which, pressumably has been submitted to some Journal.

Finally, as far as the two joint papers by W. Oevel and myself, note that most of the citations in literature are to both the papers by W. Oevel and myself; however, in the databases this is not reported, and, conversely, the citation is counted only for the ÔPart IÕ paper all the times when the citation is to ÒPart I and Part IIÓ in one single bibliography item.

              Citing Papers

  1. WOS:000278182800046 MR2666992 (2011k:37103)
    Cheng, Jipeng ; He, Jingsong ; Hu, Sen . The ÓghostÓ symmetry of the BKP hierarchy. J. Math. Phys. 51 (2010), no. 5, 053514, 19 pp.
  2. WOS:000276879800003   MR2647313 (2011e:37159)
    Hentosh, Oksana Ye. The Lax integrable differential-difference dynamical systems on extended phase spaces. SIGMA Symmetry Integrability Geom. Methods Appl. 6 (2010), Paper 034, 14 pp.
  3. WOS:000266443700024  MR2531302 (2010g:35272)
    Liu, Xiaojun ; Lin, Runliang ; Jin, Bo ; Zeng, Yunbo . A generalized dressing approach for solving the extended KP and the extended mKP hierarchy. J. Math. Phys. 50 (2009), no. 5, 053506, 14 pp.
  4. WOS:000264819400006     MR2504632 (2010g:35014) 
    Hu, Xing-Biao ; Lou, Sen-Yue ; Qian, Xian-Min . Nonlocal symmetries for bilinear equations and their applications. Stud. Appl. Math. 122 (2009), no. 3, 305Ð324.
  5. WOS:000260028100013     MR2455845 (2009i:37188)  
    Liu, Xiaojun ; Zeng, Yunbo ; Lin, Runliang . An extended two-dimensional Toda lattice hierarchy and two-dimensional Toda lattice with self-consistent sources. J. Math. Phys. 49 (2008), no. 9, 093506, 19 pp.
  6. WOS:000260028100005     MR2455837 (2010a:37131)  
    Fontanelli, Laura ; Lorenzoni, Paolo ; Pedroni, Marco ; Zubelli, Jorge P. Bi-Hamiltonian aspects of a matrix Harry Dym hierarchy. J. Math. Phys. 49 (2008), no. 9, 092901, 15 pp.
  7. WOS:000238422400011       MR2235642 (2007m:37179)
    Xiao, Ting ; Zeng, Yunbo . BŠcklund transformations for the constrained dispersionless hierarchies and dispersionless hierarchies with self-consistent sources. Inverse Problems 22 (2006), no. 3, 869Ð879.
  8. WOS:000228487500032     MR2131248 (2005m:37156)
    Casati, Paolo ; Lorenzoni, Paolo ; Ortenzi, Giovanni ; Pedroni, Marco . On the local and nonlocal Camassa-Holm hierarchies. J. Math. Phys. 46 (2005), no. 4, 042704, 8 pp.
  9. WOS:000296521900033       Wang, J., Hu, H., Yu, J.
    A new (2+1)-dimensional generalization of the modified Korteweg-deVries equation and its infinitely many symmetries (2011) Journal of Mathematical Physics, 52 (10), art. no. 103704, . DOCUMENT TYPE: Article SOURCE: Scopus
  10. WOS:000287200600013   Liu, X., Gao, C. Generalized dressing method for the extended two-dimensional Toda lattice hierarchy and its reductions (2011) Science China Mathematics, 54 (2), pp. 365-380. DOCUMENT TYPE: Article SOURCE: Scopus
  11. WOS:000283300100023     Lin, R., Peng, H., Ma–as, M. The q-deformed mKP hierarchy with self-consistent sources, Wronskian solutions and solitons (2010) Journal of Physics A: Mathematical and Theoretical, 43 (43), art. no. 434022, . DOCUMENT TYPE: Article SOURCE: Scopus
  12. WOS:000276204400006    Ma, W.-X. An extended Harry Dym hierarchy (2010) Journal of Physics A: Mathematical and Theoretical, 43 (16), art. no. 165202, . DOCUMENT TYPE: Article SOURCE: Scopus
  13. WOS:000271150500023      Tian, K., Hu, X.-B. Negative semi-discrete KP and BKP hierarchies via nonlocal symmetries (2009) Journal of Physics A: Mathematical and Theoretical, 42 (45), art. no. 454022, . DOCUMENT TYPE: Article SOURCE: Scopus
  14. WOS:71726200010,  2-s2.0-0040577087   Oevel, W., Carillo, S. (1998), Squared eigenfunction symmetries for soliton equations: Part II. Journal of Mathematical Analysis and Applications, 217(1), 179-199. Retrieved from www.scopus.com
  15. WOS:000257167000007     Jia, M., Li, J.-H., Lou, S.Y. The bilinear negative Kadomtsev-Petviashvili system and its Kac-Moody-Virasoro symmetry group (2008) Journal of Physics A: Mathematical and Theoretical, 41 (27), art. no. 275204, . DOCUMENT TYPE: Article SOURCE: Scopus
  16. WOS:000234726700017     Xiao, T., Zeng, Y. The constrained dispersionless mKP hierarchy and the dispersionless mKP hierarchy with self-consistent sources (2006) Physics Letters, Section A: General, Atomic and Solid State Physics, 349 (1-4), pp. 128-134. DOCUMENT TYPE: Article SOURCE: Scopus
  17. WOS:000275974500016     A NON-COMMUTATIVE OPERATOR-HIERARCHY OF BURGERS EQUATIONS AND B€CKLUND TRANSFORMATIONS Author(s): Carillo, Sandra; Schiebold, Cornelia Book Editor(s): DeBernardis, E; Spigler, R; Valente, V, APPLIED AND INDUSTRIAL MATHEMATICS IN ITALY III Book Series: Series on Advances in Mathematics for Applied Sciences Volume: 82 Pages: 175-185 DOI: 10.1142∕9789814280303_016 Published: 2010
  18. WOS:000180061400016    Pedroni, M., Sciacca, V., Zubelli, J.P. The bi-Hamiltonian theory of the Harry Dym equation (2002) Theoretical and Mathematical Physics, 133 (2), pp. 1585-1597.
  19. WOS:000310951700009    Carillo S., Nonlinear Evolution Equations: BŠcklund Transformations and BŠcklund Charts, Acta Applicandae Mathematicae, 122, n.ro 1, 93Ð106, (2012); doi: 10.1007∕s10440 - 012 - 9729 - 8; 

Citations 2013 (not counted)

Cheng, J., He, J.
The "ghost" symmetry in the CKP hierarchy
(2014) Journal of Geometry and Physics, 80, pp. 49-57.
http://www.scopus.com/inward/record.url?eid=2-s2.0-84896331637&partnerID=40&md5=ea4fb28e8286c1ab8ae0f6dd6266a592
DOCUMENT TYPE: Article
SOURCE: Scopus

Chvartatskyi, O.I., Sydorenko, Y.M.
A new bidirectional generalization of (2+1)-dimensional matrix k-constrained Kadomtsev-Petviashvili hierarchy
(2013) Journal of Mathematical Physics, 54 (11), art. no. 113508, .
http://www.scopus.com/inward/record.url?eid=2-s2.0-84888794379&partnerID=40&md5=e6769da097c23a3c8e9088a1b49da860
DOCUMENT TYPE: Article
SOURCE: Scopus

Chvartatskyi, O., Sydorenko, Yu.
Matrix generalizations of integrable systems with Lax integro-differential representations
(2013) Journal of Physics: Conference Series, 411 (1), art. no. 012010, .
http://www.scopus.com/inward/record.url?eid=2-s2.0-84874168296&partnerID=40&md5=0d6a38b89109c99fcdf7c648487f641b
DOCUMENT TYPE: Conference Paper
SOURCE: Scopus

Cheng, J., He, J.
On the squared eigenfunction symmetry of the Toda lattice hierarchy
(2013) Journal of Mathematical Physics, 54 (2), art. no. 023511, .
http://www.scopus.com/inward/record.url?eid=2-s2.0-84874744682&partnerID=40&md5=7f43d5a10d2c01305fab91095c9523c9
DOCUMENT TYPE: Article
SOURCE: Scopus

Cheng, J.-P., He, J.-S.
Squared eigenfunction symmetries for the BTL and CTL hierarchies
(2013) Communications in Theoretical Physics, 59 (2), pp. 131-136.
http://www.scopus.com/inward/record.url?eid=2-s2.0-84874858755&partnerID=40&md5=202a362d9ace6f86b526f680749ad800
DOCUMENT TYPE: Article
SOURCE: Scopus

4.5 Citations of C. Rogers, S. Carillo, On reciprocal properties of the Caudrey-Dodd-Gibbon and Kaup-Kupershmidt hierarchies,  Physica Scripta, 36, (1987), 865Ð869

The paper has been cited 33 (+4) times: the result is obtained considering all possible sources. Some further references which are not indexed by the Scopus and/or ISI daabases are listed t the end, but not used in the computation.

Note that the number of citations is higher than that one in each of the Databases I used (MathSciNet, Scopus, Web of Science and, occasionally, ZentralBlatt Math) further to look on the web, in general. As a consequence of retrieving also those citations non listed on the databases, but available online, the H-C index is

H-C=6  since (4x33)/26=5.08

                                        Citing Papers

  1. WOS:000268614500029,  2-s2.0-68749111018  Carillo, Sandra ; Schiebold, Cornelia . Noncommutative Korteweg-de Vries and modified Korteweg-de Vries hierarchies via recursion methods. J. Math. Phys. 50 (2009), no. 7, 073510, 14 pp.
  2. WOS:000178095500027, 2-s2.0-0035534465   
    Dye, J. M. ; Parker, A. A bidirectional Kaup-Kupershmidt equation and directionally dependent solitons. J. Math. Phys. 43 (2002), no. 10, 4921Ð4949.
  3. WOS:000177222300008, 2-s2.0-0034782643   MR1919908 (2003e:37093)
    Foursov, Mikhail V. ; Moreno Maza, Marc . On computer-assisted classification of coupled integrable equations. Computer algebra (London, ON, 2001). J. Symbolic Comput. 33 (2002), no. 5, 647Ð660.
  4. WOS:000168829800014, 2-s2.0-0035534465   MR1821879 (2002f:37113)
    Dye, J. M. ; Parker, A. On bidirectional fifth-order nonlinear evolution equations, Lax pairs, and directionally dependent solitary waves. J. Math. Phys. 42 (2001), no. 6, 2567Ð2589.
  5. WOS:000089208000013, 2-s2.0-0000259839    MR1779829 (2001i:35246) 
    Musette, Micheline ; Verhoeven, Caroline . Nonlinear superposition formula for the Kaup-Kupershmidt partial differential equation. Phys. D 144 (2000), no. 1-2, 211Ð220.
  6. WOS:000084887400003, 2-s2.0-0346684395    MR1738765 (2001d:35168)
    Parker, A. On soliton solutions of the Kaup-Kupershmidt equation. II. ÓAnomalousÓ N-soliton solutions. Phys. D 137 (2000), no. 1-2, 34Ð48.
  7. WOS:000084887400002, 2-s2.0-0345846114    MR1738764 (2000m:35162)
    Parker, A. On soliton solutions of the Kaup-Kupershmidt equation. I. Direct bilinearisation and solitary wave. Phys. D 137 (2000), no. 1-2, 25Ð33.
  8. WOS:000310951700009, 2-s2.0-84869493865    Carillo S., Nonlinear Evolution Equations: BŠcklund Transformations and BŠcklund Charts, Acta Applicandae Mathematicae, 122, n.ro 1, pp. 93-106, (2012); doi: 10.1007/s10440-012-9729-8. 
  9. WOS:000313870000048   A. Biswas, G. Ebadi, H. Triki, A. Yildirim, and N. Yousefzadeh, Topological Soliton and Other Exact Solutions to KdVCaudreyDoddGibbon Equation, Results. Math., Online First 2012 Springer Basel AG DOI 10.1007/s00025-011-0226-6
  10. WOS:000089034500025   
    Musette, Micheline ; Verhoeven, Caroline . A nonlinear superposition formula for the Kaup-Kupershmidt partial differential equation. PROCEEDINGS OF THE WORKSHOP ON NONLINEARITY, INTEGRABILITY AND ALL THAT: TWENTY YEARS AFTER NEEDS '79,  Boiti, M; Martina, L; Pempinelli, F; Prinari, B; Soliani, G Ed.s.
  11. WOS:000299847700035, 2-s2.0-84862814743    Yunling Ma and Xianguo Geng, Darboux and Baecklund transformations of the bidirectional SawadaKotera equation Applied Mathematics and Computation 2012
  12. WOS:000281535300016, 2-s2.0-78649692855  C. Rogers, W. K. Schief. and A Szereszewski, Loop soliton interaction in an integrable nonlinear telegraphy model: reciprocal and Bcklund transformations, Journal of Physics A: Mathematical and Theoretical, 43, n.ro 38, 16 pp. (2010) 43 385210 doi:10.1088/1751-8113/43/38/385210
  13. WOS:000173055900001, 2-s2.0-0035528138   V. E. Adler, V. G. Marikhin, A. B. Shabat, Lagrangian Chains and Canonical BŠcklund Transformations, Theoretical and Mathematical Physics, Vol. 129, No. 2, pp. 14481465, 2001
  14. WOS:000088459700006, 2-s2.0-0034709841   Hon-Wah Tam and Xing-Biao Hu, Two integrable differential-difference equations exhibiting soliton solutions of the KaupKupershmidt equation type, Physics Letters A, 3, n.ro 24, pp. 174Ð183, 2000 272 174
  15. WOS:000083810800002, 2-s2.0-0000728855   Xing-Biao Hu, Dao-Liu Wang, Xian-Min Qian, Soliton solutions and symmetries of the 2+1 dimensional KaupKupershmidt equation, Physics Letters A, Volume 262, Issue 6, 15 November 1999, Pages 409-415, ISSN 0375-9601, 10.1016/S0375-9601(99)00683-0.
  16. WOS:A1993MA43600003, 2-s2.0-0003163060       Sen-yue Lou, Recursion operator and symmetry structure of the kawamoto-type equation, Physics Letters A, Volume 181, Issue 1, 27 September 1993, Pages 13-16, ISSN 0375-9601, 10.1016/0375-9601(93)91116-M.
  17. 2-s2.0-77956800526,    B.G. Konopelchenko, C. Rogers, BŠcklund and Reciprocal Transformations: Gauge Connections, In: W.F. Ames and C. Rogers, Editor(s), Mathematics in Science and Engineering, Elsevier, 1992, Volume 185, Pages 317-362, ISSN 0076-5392, ISBN 9780120567522, 10.1016/S0076-5392(08)62803-9.
  18. 2-s2.0-77957236924  M.C. Nucci, Riccati-type Pseudopotentials and Their Applications, In: W.F. Ames and C. Rogers, Editor(s), Mathematics in Science and Engineering, Elsevier, 1992, Volume 185, Pages 399-436, ISSN 0076-5392, ISBN 9780120567522, 10.1016/S0076-5392(08)62805-2.
  19. WOS:A1992HA16200025  Fuchssteiner, B, Schulze, T. and Carillo, S., Explicit solutions for the Harry Dym equation, Journal of Physics A: Mathematical and General 25, (1992), 223-230,
  20. WOS:A1989AC84300027  S. Carillo and B. Fuchssteiner, The abundant symmetry structure of hierarchies of nonlinear equations obtained by reciprocal links, Journal of Mathematical Physics, 30, (1989), 1606-1613.
  21. WOS:A1989AJ92500009, 2-s2.0-0000018563   M C Nucci, PainlevŽ property and pseudopotentials for nonlinear evolution equations, Journal of Physics A: Mathematical and General, 22, n.15, 2897Ð2913 (1989).
  22. WOS:A1993LQ21100002  W. Oevel, C. Rogers, Gauge transformations and reciprocal links in 2+1 dimensions, Rev. Math. Phys. 5, no. 2, 299Ð330 (1993).
  23. WOS:A1989T085300005   Fuchssteiner B., Carillo S., Soliton structure versus singularity analysis: third order completely integrable non linear differential equations in 1 + 1-dimensions,  Physica A, 154, (1989), 467-510, doi:10.1016/0378-4371(89)90260-4
  24. WOS:000177222300008, 2-s2.0-0036331163      M.V. Foursov and M.M. Maza, On computer-assisted classification of coupled integrable equations. In Proceedings of the 2001 international symposium on Symbolic and algebraic computation (ISSAC Õ01). ACM, New York, NY, USA, 129Ð136, (2001). DOI=10.1145/384101.384120
  25. WOS:000186633400001  R. Conte, Exact solutions of nonlinear partial differential equations by singularity analysis, in Direct and Inverse Methods in nonlinear evolution equations, pp. 1Ð83, Lecture Notes in Physics Volume 632, Springer, Berlin, 2003,   ISBN: 978-3-540-20087-1 (Print) 978-3-540-39808-0 (Online) (2003)
  26. WOS:A1990DV53200015   Carillo S., Fuchssteiner B.,  The Action-Angle Transformation for Soliton Equations,  Physica A, 166, (1990), 651Ð676,
  27. WOS:000275974500016  Carillo S., C. Schiebold A non-commutative operator-hierarchy of Burgers equations and BŠcklund transformations, in Applied and Industrial Mathematics in Italy III: Selected Contributions from the 9th SIMAI Conference, E. De Bernardis, R. Spigler e V. Valente Ed.s, SERIES ON ADVANCES IN MATHEMATICS FOR APPLIED SCIENCES, vol.82, pp. 175 Ð185, World Scientific Pubbl., Singapore, 2010; doi: 10.1142/9789814280303-0016, ISBN: 978-981-4280-29-7, 981-4280-29-1; WOS:000275974500016, MathSciNet, ZentralblattMATH.
  28. WOS:A1995RF69700003, 2-s2.0-25444455943   C. Rogers, W.K. Schief, M.P. Stallybrass, Initial/boundary value problems and Darboux-Levi-type transformations associated with a 2 + 1-dimensional eigenfunction equation, International Journal of Non-Linear Mechanics, Volume 30, Issue 3, May 1995, Pages 223-233, ISSN 0020-7462, 10.1016/0020-7462(94)00045-C.
  29. WOS:000077613900005, 2-s2.0-0011363653   E.V Ferapontov, C Rogers, W.K Schief, Reciprocal Transformations of Two-Component Hyperbolic Systems and Their Invariants, Journal of Mathematical Analysis and Applications, Volume 228, Issue 2, 15 December 1998, Pages 365-376, ISSN 0022-247X, 10.1006/jmaa.1998.6131.
  30. WOS:000186633400003   M. Musette, Nonlinear superposition formulae of integrable partial differential equations by the singular manifold method, in Direct and Inverse Methods in Nonlinear Evolution Equations, Lecture Notes in Physics Volume 632, 2003, pp 137-170
  31. WOS:000165239600025, 2-s2.0-0034238991   A. Parker, On regular and anomalous solitons of fifth-order equations and an iteration method, Reports on Mathematical Physics, Volume 46, Issues 12, AugustOctober 2000, Pages 217-224, ISSN 0034-4877, 10.1016/S0034-4877(01)80026-4.(compariva 2 volte)
  32. WOS:000076187800037, 2-s2.0-0032357771 
    Musette, M (Musette, M); Conte, R (Conte, R), Backlund transformation of partial differential equations from the Painleve-Gambier classification. I. Kaup-Kupershmidt equation, JOURNAL OF MATHEMATICAL PHYSICS  Volume: 39  Issue: 10  Pages: 5617-5630  DOI: 10.1063/1.532554  Published: OCT 1998,  ISSN: 0022-2488.
  33. WOS:000304365400001, 2-s2.0-84882306740   E. Musso, Symmetry, Integrability and Geometry: Methods and Applications SIGMA 8 (2012), 030, 20 pages Motions of Curves in the Projective Plane Inducing the Kaup - Kupershmidt Hierarchy Published online May 24, 2012.
  34. Carillo S., BŠcklund Charts & Applications, Proceedings WASCOM 2007, 14th International Conference on Waves and Stability in Continuous Media, N. Manganaro, R. Monaco, S. Rionero e T. Ruggeri, Ed.s, World Scientific Pubbl., Singapore, (2008), pp. 128-134; doi:10.1142/9789812772350_0020
  35. Carillo S.,  Third Order Nonlinear Hamiltonian Systems: Some remarks on the Action-Angle transformation,  in: XIXth International Conference Differential Geometrical Methods in Theoretical Physics,  Proceedings,  Bartocci C., Bruzzo U., Cianci R. eds,  Springer-Verlag, (1991), 375-379, doi:10.1007/3-540-53763-5_73
  36. M. Musette, Painleve' analysis for nonlinear partial differential equations CRM Ser. Math. Phys., pp.517Ð572, Springer, New York, 1999
  37. R. Conte, M. Musette, The PainlevŽ Handbook Springer, Dordrecht, 2008. xxiv+256 pp. ISBN: 978-1-4020-8490-4

Citations 2013 (not counted)

Biswas, A., Ebadi, G., Triki, H., Yildirim, A., Yousefzadeh, N.
Topological Soliton and Other Exact Solutions to KdV-Caudrey-Dodd-Gibbon Equation
(2013) Results in Mathematics, 63 (1-2), pp. 687-703. Cited 2 times.
http://www.scopus.com/inward/record.url?eid=2-s2.0-84872655498&partnerID=40&md5=ce19dd4101a0432ae60aa2bd2def7f70
DOCUMENT TYPE: Article
SOURCE: Scopus

4.7 Citations of Oevel W., Carillo S.   for Soliton Equations: Part II,  J. Math. Anal. and Appl., 217, (1998), 179Ð199; doi:10.1006/jmaa.1997.5708

H-C=4  since (4x14)/15=3.73

The paper has been cited 14 times: the result is obtained considering all possible sources. I did check that the paper appears in all the papers listed here below.

Note that the number of citations is higher than that one in each of the Databases I used (MathSciNet, Scopus and Web of Science). As a consequence of retrieving also those citations non listed on the databases,

Finally, note that most of the citations in literature are to both the papers by W. Oevel and myself; however, this is not reported in the databases where the citation all the times when the citation is to ÒPart I and Part IIÓ in one single bibliography item, it is counted for ÒPart IÓ only. 

              Citing Papers

  1. WOS:000278182800046      MR2666992 (2011k:37103)
    Cheng, Jipeng ; He, Jingsong ; Hu, Sen . The ÓghostÓ symmetry of the BKP hierarchy. J. Math. Phys. 51 (2010), no. 5, 053514, 19 pp.
  2. WOS:000276879800003        MR2647313 (2011e:37159)
    Hentosh, Oksana Ye. The Lax integrable differential-difference dynamical systems on extended phase spaces. SIGMA Symmetry Integrability Geom. Methods Appl. 6 (2010), Paper 034, 14 pp.
  3. WOS:000266443700024       MR2531302 (2010g:35272)
    Liu, Xiaojun ; Lin, Runliang ; Jin, Bo ; Zeng, Yunbo . A generalized dressing approach for solving the extended KP and the extended mKP hierarchy. J. Math. Phys. 50 (2009), no. 5, 053506, 14 pp.
  4. WOS:000264819400006          MR2504632 (2010g:35014) 
    Hu, Xing-Biao ; Lou, Sen-Yue ; Qian, Xian-Min . Nonlocal symmetries for bilinear equations and their applications. Stud. Appl. Math. 122 (2009), no. 3, 305Ð324.
  5. WOS:000260028100005      MR2455837 (2010a:37131) 
    Fontanelli, Laura ; Lorenzoni, Paolo ; Pedroni, Marco ; Zubelli, Jorge P. Bi-Hamiltonian aspects of a matrix Harry Dym hierarchy. J. Math. Phys. 49 (2008), no. 9, 092901, 15 pp.
  6. WOS:000228487500032      MR2131248 (2005m:37156)
    Casati, Paolo ; Lorenzoni, Paolo ; Ortenzi, Giovanni ; Pedroni, Marco . On the local and nonlocal Camassa-Holm hierarchies. J. Math. Phys. 46 (2005), no. 4, 042704, 8 pp.
  7. WOS:000287200600013    Liu, X., Gao, C. Generalized dressing method for the extended two-dimensional Toda lattice hierarchy and its reductions (2011) Science China Mathematics, 54 (2), pp. 365-380. DOCUMENT TYPE: Article SOURCE: Scopus
  8. WOS:000287233200001   JP Cheng, JS He, LH Wang, A General Formula of Flow Equations for Harry-Dym Hierarchy, Communications in Theoretical Physics 2011, 55(02) 193-198 PACS: ISSN: 0253-6102 CN: 11-2592/O3
  9. WOS:000276204400006    Ma, W.-X. An extended Harry Dym hierarchy (2010) Journal of Physics A: Mathematical and Theoretical, 43 (16), art. no. 165202, . DOCUMENT TYPE: Article SOURCE: Scopus
  10. WOS:000271150500023      Tian, K., Hu, X.-B. Negative semi-discrete KP and BKP hierarchies via nonlocal symmetries (2009) Journal of Physics A: Mathematical and Theoretical, 42 (45), art. no. 454022, . DOCUMENT TYPE: Article SOURCE: Scopus
  11. WOS: 000071726200009, Scopus 2-s2.0-0039394289  Oevel, W., Carillo, S. (1998), Squared eigenfunction symmetries for soliton equations: Part I. Journal of Mathematical Analysis and Applications, 217(1), 161-178. Retrieved from www.scopus.com
  12. WOS:000275974500016     A NON-COMMUTATIVE OPERATOR-HIERARCHY OF BURGERS EQUATIONS AND B€CKLUND TRANSFORMATIONS Author(s): Carillo, Sandra; Schiebold, Cornelia Book Editor(s): DeBernardis, E; Spigler, R; Valente, V, APPLIED AND INDUSTRIAL MATHEMATICS IN ITALY III Book Series: Series on Advances in Mathematics for Applied Sciences Volume: 82 Pages: 175-185 DOI: 10.1142∕9789814280303_016 Published: 2010
  13.  WOS:000180061400016    Pedroni, M., Sciacca, V., Zubelli, J.P. The bi-Hamiltonian theory of the Harry Dym equation (2002) Theoretical and Mathematical Physics, 133 (2), pp. 1585-1597.
  14. WOS:000310951700009     Carillo S., Nonlinear Evolution Equations: BŠcklund Transformations and BŠcklund Charts, Acta Applicandae Mathematicae, 122, n.ro 1, pp. 93-106, (2012); doi: 10.1007∕s10440 - 012 - 9729 - 8;  

Citations 2013 (not counted)

Remark: the following papers cite both Part I as well as Part II, i.e. the two papers by W. Oevel and S.Carillo; however, in the Scopus database it appears twice Part I in both the cases: it is often happened.
Cheng, J., He, J. Corrections are in progress in both Web of Science as well as Scopus Databases.

On the squared eigenfunction symmetry of the Toda lattice hierarchy
(2013) Journal of Mathematical Physics, 54 (2), art. no. 023511, .
http://www.scopus.com/inward/record.url?eid=2-s2.0-84874744682&partnerID=40&md5=7f43d5a10d2c01305fab91095c9523c9
DOCUMENT TYPE: Article
SOURCE: Scopus


Cheng, J.-P., He, J.-S.
Squared eigenfunction symmetries for the BTL and CTL hierarchies
(2013) Communications in Theoretical Physics, 59 (2), pp. 131-136.
http://www.scopus.com/inward/record.url?eid=2-s2.0-84874858755&partnerID=40&md5=202a362d9ace6f86b526f680749ad800
DOCUMENT TYPE: Article
SOURCE: Scopus

4.7 Citations of

WOS:A1982NS86900022, 2-s2.0-0008859965  Bassani F., Quattropani A., Carillo S.,

Two photon transition to excited states in atomic hydrogen,  Phys. Rev. A  25,  (1982), 3079-3089.

The paper has been cited 46 times in ISI (follow this link): the result is obtained considering ONLY Web of Science, where the paper is  indexed (I thought it was not since I could NON find this paper since SAPIENZA University's subscription starts in 1985), there are 46 citations (1982-2012). Further citations indexed by the Scopus and/or ISI daabases can be found. However, there is no need to look for further ones since  H-C=6  since (4x46)/31=5.93

ISI_citationsPhysRevA25


4.8 Citations of Carillo S., Fuchssteiner B.,  The abundant symmetry structure of non linear equations obtained by reciprocal links,  J. Math. Phys., 30, (1989), 1606Ð1613, doi:10.1063/1.528604  A.M.S. 58G35  35Q20  58F07  58G37

The paper has been cited 25 times rstricting to papers which are comprised in the Scopus and/or ISI databases, and hence, the related index is:

H-C=5  since (4x28)/24=4.66

I did check that the citation appears in all the articles listed here below by inspection looking in the reference list of each paper in the list. Note that the number of citations is higher than that one in each of the Databases I used (Scopus or Web of Science). Thte data can be easily checked direcly looking into the Reference Section of the papers here enlisted. (ISI code `WOS:', Scopus code `2-s2')

              Citing Papers

  1. WOS:000304827000021, 2-s2.0-84861993141  The transformations between N = 2 supersymmetric Korteweg-de Vries and Harry Dym equations Kai Tian, Liu, Q.P., J. Math. Phys. 53, 053503 (2012) 
  2. WOS:A1994NJ53300027  Sen-yue Lou, Symmetries of the KdV equation and four hierarchies of the integrodifferential KdV equations J. Math. Phys. 35, 2390 (1994) 
  3. WOS:A1994NJ53300022  Pin Han, S Lou, Abundant Symmetry Structure of the Kaup-Kupershmidt Hierarchies, Chinese Physics Letters 10, 257 (1993)
  4. WOS:A1993MA43600003  Recursion operator and symmetry structure of the kawamoto-type equation Sen-yue Lou, Physics Letters A 181, 13 (1992)
  5. WOS:A1992JD89900011, 2-s2.0-4244038695     S Yu Sakovich, The Painleve property transformed, Journal of Physics A Mathematical and General 25 L833 (1992)
  6. WOS:A1993KY84200004, 2-s2.0-26744466122     S Y Sakovich, On Miura transformations of evolution equations, Journal of Physics A Mathematical and General 26, L369 (1993)
  7. WOS:A1992HA16200025   Fuchssteiner, B, Schulze, T. and Carillo, S.,  Explicit solutions for the Harry Dym equation,  J. Phys. A: Math. Gen., 25, 223-230, (1992)
  8. WOS:000166114700019, 2-s2.0-0034670489   Carillo, S. (2000). A novel BŠcklund invariance of a nonlinear differential equation. Journal of Mathematical Analysis and Applications, 252(2), 828-839. Retrieved from www.scopus.com
  9. WOS:291106000032, 2-s2.0-79957899011   Carillo, S., Schiebold, C. (2011). Matrix korteweg-de vries and modified korteweg-de vries hierarchies: Noncommutative soliton solutions. Journal of Mathematical Physics, 52(5) Retrieved from www.scopus.com
  10. WOS:268614500029, SCOPUS 2-s2.0-68749111018   Carillo, S., Schiebold, C. (2009). Noncommutative korteweg-de vries and modified korteweg-de vries hierarchies via recursion methods. Journal of Mathematical Physics, 50(7) Retrieved from www.scopus.com
  11. WOS:000172301400008    Dimakis, A., Mller-Hoissen, F. (2001). Bicomplexes and BŠcklund transformations. Journal of Physics A: Mathematical and General, 34(43), 9163-9194. Retrieved from www.scopus.com
  12. WOS:A1996VZ69700009   Lou, S. -. (1996). Symmetry algebras and group invariant solutions of the kawamoto-type equations. Communications in Theoretical Physics, 26(3), 311-318. Retrieved from www.scopus.com
  13. WOS: 000071726200009, Scopus 2-s2.0-0039394289  Oevel, W., Carillo, S. (1998). Squared eigenfunction symmetries for soliton equations: Part I. Journal of Mathematical Analysis and Applications, 217(1), 161-178. Retrieved from www.scopus.com
  14. WOS:71726200010, 2-s2.0-0040577087    Oevel, W., Carillo, S. (1998). Squared eigenfunction symmetries for soliton equations: Part II. Journal of Mathematical Analysis and Applications, 217(1), 179-199. Retrieved from www.scopus.com
  15. WOS:A1996VF08800002,  2-s2.0-22244482803      Benno Fuchssteiner, Some tricks from the symmetry-toolbox for nonlinear equations: Generalizations of the Camassa-Holm equation, Physica D: Nonlinear Phenomena, Volume 95, Issues 34, 1 September 1996, Pages 229-243, ISSN 0167-2789.  
  16. WOS:A1993LU12200011       Sen-yue Lou, Wei-zhong Chen, Inverse recursion operator of the AKNS hierarchy, Physics Letters A, Volume 179, Issues 4-5, 16 August 1993, Pages 271-274, ISSN 0375-9601,
  17. WOS:A1991FV24600011    B. Fuchssteiner, J. Phys. Soc. Jpn. 60 (1991) pp. 1473-1496 Linear Aspects in the Theory of Solitons and Nonlinear Integrable Equations    
  18. WOS:000189013100001, 2-s2.0-1042302422   Symmetries and Strong Symmetries of the (3+1)-Dimensional Burgers Equation Lian Zeng-Ju and Lou Sen-Yue 2004 Chinese Phys. Lett. 21 219  
  19. WOS:000087191500004, 2-s2.0-0034369873   MR1757007 (2001i:37112)
    Zubelli, Jorge P. ; Valerio Silva, D. S. Rational solutions of the master symmetries of the KdV equation. Comm. Math. Phys. 211 (2000), no. 1, 85Ð109.
  20. WOS:302022500003, 2-s2.0-84858822229  MR2905320 (Review)
    Carillo, Sandra ; Schiebold, Cornelia . On the recursion operator for the noncommutative Burgers hierarchy. J. Nonlinear Math. Phys. 19 (2012), no. 1, 1250003, 11 pp.
  21. WOS:A1994NC06300004    C. Rogers, M.P. Stallybrass, P. Vassiliou, An invariance of the (2 + 1)-dimensional Harry-Dym equation: Application to initial/boundary value problems, International Journal of Non-Linear Mechanics, Volume 29, Issue 2, March 1994, Pages 145-154, ISSN 0020-7462, 
  22. WOS:A1994PW33700010   Sen-Yue Lou, Symmetries and lie algebras of the Harry Dym hierarchy, Chaos, Solitons & Fractals, Volume 4, Issue 10, October 1994, Pages 1961-1964, ISSN 0960-0779, 10.1016/0960-0779(94)90010-8.     
  23. WOS:000306624600002 Kai Tian, Q.P. Liu, Two new supersymmetric equations of Harry Dym type and their supersymmetric reciprocal transformations, Physics Letters A, Volume 376, Issue 35, 16 July 2012, Pages 2334-2340, ISSN 0375-9601, 10.1016/j.physleta.2012.06.003.
  24. WOS:000310951700009    Carillo S., Nonlinear Evolution Equations: BŠcklund Transformations and BŠcklund Charts, Acta Applicandae Mathematicae, 122, n.ro 1, pp. 93-106, (2012); doi: 10.1007∕s10440 - 012 - 9729 - 8;  
  25. WOS:A1989T085300005, 2-s2.0-0002407153  B. Fuchssteiner, S. Carillo, Soliton structure versus singularity analysis: Third-order completely intergrable nonlinear differential equations in 1 + 1-dimensions, Physica A: Statistical Mechanics and its Applications, Volume 154, Issue 3, 15 January 1989, 467Ð510, ISSN 0378-4371, 10.1016/0378-4371(89)90260-4.
  26. WOS:A1990BS60Z00033   CARILLO, S; FUCHSSTEINER, B
    NON COMMUTATIVE SYMMETRIES AND NEW SOLUTIONS OF THE HARRY DYM EQUATION
     DEGASPERIS, A; FORDY, AP; LAKSHMANAN, M Ed.s
    NONLINEAR EVOLUTION EQUATIONS : INTEGRABILITY AND SPECTRAL METHODS, Pages: 351-365   Published: 1990
  27. WOS:A1990DV53200015,    2-s2.0-4243264964  Fuchssteiner B., Carillo S.,
    The Action-Angle Transformation for Soliton  Equations,  Physica A, 166,  1990, 651-676.
  28. WOS:A1993BA20B00008 Carillo S., Fuchssteiner B., Some remarks on a Class of Ordinary Differential
     Equations: the Riccati   Property, in: Modern Group Analysis: Advanced Analytical Methods in Mathematical
     Physics, Ibragimov N.H., Torrisi M., Valenti A. eds, Kluwer Academic Pubbl. (1993), 85-97.

  29.  S Carillo, C Schiebold, Recursion techniques and explicit solutions of integrable noncommutative hierarchies, in  - Waves and Stability in Continuous , 2010 - A. Greco, S. Rionero, T Ruggeri Ed.s, 
  30. The Bispectral Problem, Rational Solutions of the Master Symmetry Flows, and Bihamiltonian Systems JP Zubelli - CRM Proceedings Lecture Notes, 1998


4.9 Citations of Oevel W., Carillo S.   for Soliton Equations: Part II,  J. Math. Anal. and Appl., 217, (1998), 179Ð199; doi:10.1006/jmaa.1997.5708

H-C=4  since (4x14)/15=3.73

The paper has been cited 14 times: the result is obtained considering all possible sources. I did check that the paper appears in all the papers listed here below.

Note that the number of citations is higher than that one in each of the Databases I used (MathSciNet, Scopus and Web of Science). As a consequence of retrieving also those citations non listed on the databases,

Finally, note that most of the citations in literature are to both the papers by W. Oevel and myself; however, this is not reported in the databases where the citation all the times when the citation is to ÒPart I and Part IIÓ in one single bibliography item, it is counted for ÒPart IÓ only. 

              Citing Papers

  1. WOS:000278182800046      MR2666992 (2011k:37103)
    Cheng, Jipeng ; He, Jingsong ; Hu, Sen . The ÓghostÓ symmetry of the BKP hierarchy. J. Math. Phys. 51 (2010), no. 5, 053514, 19 pp.
  2. WOS:000276879800003        MR2647313 (2011e:37159)
    Hentosh, Oksana Ye. The Lax integrable differential-difference dynamical systems on extended phase spaces. SIGMA Symmetry Integrability Geom. Methods Appl. 6 (2010), Paper 034, 14 pp.
  3. WOS:000266443700024       MR2531302 (2010g:35272)
    Liu, Xiaojun ; Lin, Runliang ; Jin, Bo ; Zeng, Yunbo . A generalized dressing approach for solving the extended KP and the extended mKP hierarchy. J. Math. Phys. 50 (2009), no. 5, 053506, 14 pp.
  4. WOS:000264819400006          MR2504632 (2010g:35014) 
    Hu, Xing-Biao ; Lou, Sen-Yue ; Qian, Xian-Min . Nonlocal symmetries for bilinear equations and their applications. Stud. Appl. Math. 122 (2009), no. 3, 305Ð324.
  5. WOS:000260028100005      MR2455837 (2010a:37131) 
    Fontanelli, Laura ; Lorenzoni, Paolo ; Pedroni, Marco ; Zubelli, Jorge P. Bi-Hamiltonian aspects of a matrix Harry Dym hierarchy. J. Math. Phys. 49 (2008), no. 9, 092901, 15 pp.
  6. WOS:000228487500032      MR2131248 (2005m:37156)
    Casati, Paolo ; Lorenzoni, Paolo ; Ortenzi, Giovanni ; Pedroni, Marco . On the local and nonlocal Camassa-Holm hierarchies. J. Math. Phys. 46 (2005), no. 4, 042704, 8 pp.
  7. WOS:000287200600013    Liu, X., Gao, C. Generalized dressing method for the extended two-dimensional Toda lattice hierarchy and its reductions (2011) Science China Mathematics, 54 (2), pp. 365-380. DOCUMENT TYPE: Article SOURCE: Scopus
  8. WOS:000287233200001   JP Cheng, JS He, LH Wang, A General Formula of Flow Equations for Harry-Dym Hierarchy, Communications in Theoretical Physics 2011, 55(02) 193-198 PACS: ISSN: 0253-6102 CN: 11-2592/O3
  9. WOS:000276204400006    Ma, W.-X. An extended Harry Dym hierarchy (2010) Journal of Physics A: Mathematical and Theoretical, 43 (16), art. no. 165202, . DOCUMENT TYPE: Article SOURCE: Scopus
  10. WOS:000271150500023      Tian, K., Hu, X.-B. Negative semi-discrete KP and BKP hierarchies via nonlocal symmetries (2009) Journal of Physics A: Mathematical and Theoretical, 42 (45), art. no. 454022, . DOCUMENT TYPE: Article SOURCE: Scopus
  11. WOS: 000071726200009, Scopus 2-s2.0-0039394289  Oevel, W., Carillo, S. (1998), Squared eigenfunction symmetries for soliton equations: Part I. Journal of Mathematical Analysis and Applications, 217(1), 161-178. Retrieved from www.scopus.com
  12. WOS:000275974500016     A NON-COMMUTATIVE OPERATOR-HIERARCHY OF BURGERS EQUATIONS AND B€CKLUND TRANSFORMATIONS Author(s): Carillo, Sandra; Schiebold, Cornelia Book Editor(s): DeBernardis, E; Spigler, R; Valente, V, APPLIED AND INDUSTRIAL MATHEMATICS IN ITALY III Book Series: Series on Advances in Mathematics for Applied Sciences Volume: 82 Pages: 175-185 DOI: 10.1142∕9789814280303_016 Published: 2010
  13.  WOS:000180061400016    Pedroni, M., Sciacca, V., Zubelli, J.P. The bi-Hamiltonian theory of the Harry Dym equation (2002) Theoretical and Mathematical Physics, 133 (2), pp. 1585-1597.
  14. WOS:000310951700009     Carillo S., Nonlinear Evolution Equations: BŠcklund Transformations and BŠcklund Charts, Acta Applicandae Mathematicae, 122, n.ro 1, pp. 93-106, (2012); doi: 10.1007∕s10440 - 012 - 9729 - 8;  

Citations 2013 (not counted) Remark: the following papers cite both Part I as well as Part II, i.e. the two papers by W. Oevel and S.Carillo; however, in the Scopus database it appears twice Part I in both the cases: it is often happened.
Cheng, J., He, J.
On the squared eigenfunction symmetry of the Toda lattice hierarchy
(2013) Journal of Mathematical Physics, 54 (2), art. no. 023511, .
http://www.scopus.com/inward/record.url?eid=2-s2.0-84874744682&partnerID=40&md5=7f43d5a10d2c01305fab91095c9523c9
DOCUMENT TYPE: Article
SOURCE: Scopus


Cheng, J.-P., He, J.-S.
Squared eigenfunction symmetries for the BTL and CTL hierarchies
(2013) Communications in Theoretical Physics, 59 (2), pp. 131-136.
http://www.scopus.com/inward/record.url?eid=2-s2.0-84874858755&partnerID=40&md5=202a362d9ace6f86b526f680749ad800
DOCUMENT TYPE: Article
SOURCE: Scopus