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Yamilov, Ravil Islamovich

Total publications: 55 (55)
in MathSciNet: 42 (42)
in zbMATH: 36 (36)
in Web of Science: 45 (45)
in Scopus: 42 (42)
Cited articles: 49
Citations in Math-Net.Ru: 342
Citations in Web of Science: 1147
Citations in Scopus: 1082

Number of views:
This page:1162
Abstract pages:5574
Full texts:1628
References:411
Doctor of physico-mathematical sciences (2000)
Speciality: 01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date: 25.04.1957
Phone: +7 (3472) 23 33 42
Fax: +7 (3472) 22 59 36
E-mail:
Website: http://matem.anrb.ru/en/yamilovri
Keywords: integrable nonlinear partial differential and differential-difference equations; classification of integrable equations; higher (generalized) symmetries and conservation laws; Hamiltonian and Lagrangian structure; transformation theory for integrable equations; Miura, Backlund and Schlesinger tranformations.
UDC: 517.9

Subject:

The classification problem has been solved for classes of integrable (more precisely, possessing an infinite hierarchy of higher symmetries and conservation laws) equations including the differential-difference Volterra and Toda equations and also (with A. B. Shabat and A. V. Mikhailov) for a class which contains the nonlinear Schrodinger equation. The notion of a quasi-local function has been introduced (with A. V. Mikhailov) which has allowed to generalize the Symmetry Approach to the classification of integrable equations for the case of 1+2 dimensional equations. A number of papers is devoted to the transformation theory for integrable equations. In particular, a scheme of the construction of modified equations together with corresponding Miura transformations has been presented which does not use $L-A$ pairs, but only uses Miura transformations.

   
Main publications:
  • Mikhailov A. V., Shabat A. B., Yamilov R. I. Extension of the module of invertible transformations. Classification of integrable systems // Commun. Math. Phys., 1988, 115, 1–19.
  • Yamilov R. I. Classification of Toda type scalar lattices // Proc. Int. Workshop NEEDS'92, World Sci. Publ., 1993, 423–431.
  • Levi D., Yamilov R. Conditions for the existence of higher symmetries of evolutionary equations on the lattice // J. Math. Phys., 1997, 38(12), 6648–6674.

http://www.mathnet.ru/eng/person17832
http://scholar.google.com/citations?user=ZU_jeUwAAAAJ&hl=en
http://zbmath.org/authors/?q=ai:yamilov.ravil-i
https://mathscinet.ams.org/mathscinet/MRAuthorID/209927
http://elibrary.ru/author_items.asp?authorid=7584
http://www.scopus.com/authid/detail.url?authorId=6602134595

Full list of publications:
| by years | by types | by times cited in WoS | by times cited in Scopus | scientific publications | common list |



   2019
1. R. N. Garifullin, R. I. Yamilov, “An unusual series of autonomous discrete integrable equations on a square lattice”, Theoret. and Math. Phys., 200:1 (2019), 966–984  mathnet  crossref  crossref  elib  scopus (cited: 1)
2. R. N. Garifullin, G. Gubbiotti, R. I. Yamilov, “Integrable discrete autonomous quad-equations admitting, as generalized symmetries, known five-point differential-difference equations”, Journal of Nonlinear Mathematical Physics, 26:3 (2019), 333-357 , arXiv: 1810.11184  crossref  mathscinet  adsnasa  isi  scopus (cited: 1)

   2018
3. R. N. Garifullin, R. I. Yamilov and D. Levi, “Classification of five-point differential-difference equations II”, J. Phys. A: Math. Theor, 51:6 (2018), 065204 , 16 pp.  crossref  isi (cited: 2)  scopus (cited: 3)
4. Giorgio Gubbiotti, Christian Scimiterna, Ravil I. Yamilov, “Darboux Integrability of Trapezoidal $H^{4}$ and $H^{6}$ Families of Lattice Equations II: General Solutions”, SIGMA, 14 (2018), 8 , 51 pp.  mathnet (cited: 2)  crossref  isi (cited: 2)  scopus (cited: 2)
5. R. N. Garifullin, R. I. Yamilov, “On the Integrability of a Lattice Equation with Two Continuum Limits”, Mathematical physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 152, VINITI, Moscow, 2018, 159–164  mathnet  mathscinet

   2017
6. R. N. Garifullin, R. I. Yamilov, D. Levi, “Classification of five-point differential-difference equations”, J. Phys. A, Math. Theor., 50:12 (2017), 125201 (27pp)  crossref  isi (cited: 6)  scopus (cited: 7)
7. G. Gubbiotti, R. I. Yamilov, “Darboux integrability of trapezoidal $H^4$ and $H^4$ families of lattice equations I: first integrals”, J. Phys. A: Math. Theor., 50:34 (2017), 345205 , 26 pp.  crossref  isi (cited: 4)  scopus (cited: 4)
8. R. N. Garifullin, R. I. Yamilov, “On integrability of a discrete analogue of Kaup–Kupershmidt equation”, Ufa Math. Journal, 9:3 (2017), 158–164  mathnet  crossref  mathscinet  isi (cited: 3)  isi (cited: 3)  elib  elib  scopus (cited: 3)

   2016
9. R. N. Garifullin, R. I. Yamilov, D. Levi, “Non-invertible transformations of differential-difference equations”, J. Phys. A, Math. Theor., 49:37 (2016), 23 pp , IOP Publishing, Bristol  crossref  isi (cited: 5)  scopus (cited: 6)

   2015
10. R. N. Garifullin, R. I. Yamilov, “Integrable discrete nonautonomous quad-equations as Bäcklund auto-transformations for known Volterra and Toda type semidiscrete equations”, Journal of Physics: Conference Series, 621:1 (2015), 012005  crossref  isi (cited: 11)  scopus (cited: 12)
11. R. N. Garifullin, I. T. Habibullin, R. I. Yamilov, “Peculiar symmetry structure of some known discrete nonautonomous equations”, J. Phys. A, Math. Theor., 48:23 (2015), 27 , IOP Publishing, Bristol  crossref  mathscinet  zmath  isi (cited: 5)  scopus (cited: 6)

   2014
12. R. N. Garifullin, A. V. Mikhailov, R. I. Yamilov, “Discrete equation on a square lattice with a nonstandard structure of generalized symmetries”, Theoret. and Math. Phys., 180:1 (2014), 765–780  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 12)  elib  scopus (cited: 13)

   2012
13. R. N. Garifullin, R. I. Yamilov, “Examples of Darboux integrable discrete equations possessing first integrals of an arbitrarily high minimal order”, Ufimsk. matem. zhurn., 4:3 (2012), 177–183  mathnet (cited: 3)  elib (cited: 1)
14. R. N. Garifullin, R. I. Yamilov, “Generalized symmetry classification of discrete equations of a class depending on twelve parameters”, J. Phys. A, Math. Theor., 45:34 (2012), 23 , IOP Publishing, Bristol  crossref  mathscinet  zmath  isi (cited: 30)  scopus (cited: 29)

   2011
15. Decio Levi, Pavel Winternitz, Ravil I. Yamilov, “Symmetries of the Continuous and Discrete Krichever–Novikov Equation”, SIGMA, 7 (2011), 97 , 16 pp., arXiv: 1110.5021  mathnet (cited: 8)  crossref  mathscinet  isi (cited: 8)  scopus (cited: 8)
16. D. Levi, R. I. Yamilov, “Generalized Lie symmetries for difference equations”, Symmetries and integrability of difference equations. Based upon lectures delivered during the summer school, Montreal, Canada, June 8–21, 2008, Cambridge: Cambridge University Press, 2011, 160–190  zmath
17. D. Levi, R. I. Yamilov, “Generalized symmetry integrability test for discrete equations on the square lattice”, J. Phys. A, Math. Theor., 44:14 (2011), 22 , IOP Publishing, Bristol  crossref  mathscinet  zmath  isi (cited: 27)  scopus (cited: 29)

   2010
18. D. Levi, R. I. Yamilov, “Integrability test for discrete equations via generalized symmetries”, Aip Conference Proceedings, 1323, no. 1, AMER INST PHYSICS, 2010, 203  crossref  isi (cited: 1)  scopus (cited: 1)
19. D. Levi, P. Winternitz, R. I. Yamilov, “Lie point symmetries of differential-difference equations”, J. Phys. A, Math. Theor., 43:29 (2010), 14 , IOP Publishing, Bristol  crossref  mathscinet  zmath  isi (cited: 11)  scopus (cited: 13)

   2009
20. D. Levi, R. I. Yamilov, “On a nonlinear integrable difference equation on the square”, Ufimsk. matem. zhurn., 1:2 (2009), 101–105  mathnet (cited: 8)  zmath  elib (cited: 7)
21. D. Levi, R. I. Yamilov, “The generalized symmetry method for discrete equations”, J. Phys. A, Math. Theor., 42:45 (2009), 18 , IOP Publishing, Bristol  crossref  mathscinet  zmath  isi (cited: 34)  scopus (cited: 37)

   2008
22. Decio Levi, Matteo Petrera, Christian Scimiterna, Ravil Yamilov, “On Miura Transformations and Volterra-Type Equations Associated with the Adler–Bobenko–Suris Equations”, SIGMA, 4 (2008), 77 , 14 pp., arXiv: 0802.1850  mathnet (cited: 23)  crossref  mathscinet  zmath  isi (cited: 23)  scopus (cited: 22)

   2007
23. R. I. Yamilov, “Integrability conditions for an analogue of the relativistic Toda chain”, Theoret. and Math. Phys., 151:1 (2007), 492–504  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)

   2006
24. R. Yamilov, “Symmetries as integrability criteria for differential difference equations”, J. Phys. A, Math. Gen., 39:45 (2006), r541–r623 , IOP Publishing Ltd., Bristol, UK  crossref  mathscinet  zmath  isi (cited: 80)  scopus (cited: 81)

   2004
25. R. I. Yamilov, “Relativistic Toda Chains and Schlesinger Transformations”, Theoret. and Math. Phys., 139:2 (2004), 623–635  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  scopus (cited: 3)
26. R. Yamilov, D. Levi, “Integrability conditions for $n$ and $t$ dependent dynamical lattice equations”, J. Nonlinear Math. Phys., 11:1 (2004), 75–101 , Taylor & Francis, Abingdon, Oxfordshire; Atlantis Press, Paris  crossref  mathscinet  zmath  isi (cited: 9)  scopus (cited: 9)

   2001
27. D. Levi, R. Yamilov, “On the integrability of a new discrete nonlinear Schrödinger equation”, J. Phys. A, Math. Gen., 34:41 (2001), l553–l562 , IOP Publishing Ltd., Bristol, UK  crossref  mathscinet  zmath  isi (cited: 7)  scopus (cited: 7)
28. D. Levi, R. Yamilov, “Conditions for the existence of higher symmetries and nonlinear evolutionary equations on the lattice”, Algebraic methods in physics. A symposium for the 60th birthdays of Ji\ví Patera and Pavel Winternitz. Centre de Recherches Mathématiques (CRM), Montréal, Canada, January 1997, Springer, New York, 2001, 135–148  mathscinet  zmath  isi (cited: 2)

   2000
29. V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, Theoret. and Math. Phys., 125:3 (2000), 1603–1661  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 91)  elib (cited: 87)  scopus (cited: 60)
30. D. Levi, R. Yamilov, “Non-point integrable symmetries for equations on the lattice”, J. Phys. A, Math. Gen., 33:26 (2000), 4809–4823 , IOP Publishing Ltd., Bristol, UK  crossref  mathscinet  zmath  isi (cited: 3)  scopus (cited: 4)

   1999
31. D. Levi, R. Yamilov, “Dilation symmetries and equations on the lattice”, J. Phys. A, Math. Gen., 32:47 (1999), 8317–8323 , IOP Publishing Ltd., Bristol, UK  crossref  mathscinet  zmath  isi (cited: 5)  scopus (cited: 5)
32. V. E. Adler, S. I. Svinolupov, R. I. Yamilov, “Multi-component Volterra and Toda type integrable equations”, Phys. Lett., A, 254:1–2 (1999), 24–36 , Elsevier (North-Holland), Amsterdam  crossref  mathscinet  zmath  isi (cited: 68)  scopus (cited: 67)

   1998
33. A. V. Mikhailov, R. I. Yamilov, “Towards classification of $(2+1)$-dimensional integrable equations. Integrability conditions. I”, J. Phys. A, Math. Gen., 31:31 (1998), 6707–6715 , IOP Publishing Ltd., Bristol, UK  crossref  mathscinet  zmath  isi (cited: 33)  scopus (cited: 31)

   1997
34. A. V. Mikhailov, R. I. Yamilov, “On integrable two-dimensional generalizations of nonlinear Schrödinger type equations”, Physics Letters, Section A: General, Atomic and Solid State Physics, 230:5–6 (1997), 295–300 , Elsevier (North-Holland), Amsterdam  crossref  mathscinet  zmath  isi (cited: 8)  scopus (cited: 10)
35. A. B. Shabat, R. I. Yamilov, “To a transformation theory of two-dimensional integrable systems”, Phys. Lett., A, 227:1–2 (1997), 15–23 , Elsevier (North-Holland), Amsterdam  crossref  mathscinet  zmath  isi (cited: 38)  scopus (cited: 41)
36. D. Levi, R. Yamilov, “Conditions for the existence of higher symmetries of evolutionary equations on the lattice”, J. Math. Phys., 38:12 (1997), 6648–6674 , American Institute of Physics (AIP), Woodbury, NY  crossref  mathscinet  zmath  isi (cited: 104)  scopus (cited: 103)

   1996
37. I. T. Habibullin, V. V. Sokolov, R. I. Yamilov, “Multi-component integrable systems and nonassociative structures”, Nonlinear physics: theory and experiment. Nature, structure and properties of nonlinear phenomena. Proceedings of the workshop, Lecce, Italy, June 29–July 7, 1995, World Scientific, Singapore, 1996, 139–168  mathscinet  zmath
38. I. Cherdantsev, R. Yamilov, “Local master symmetries of differential-difference equations”, Symmetries and integrability of difference equations. Papers from the workshop, May 22–29, 1994, Estérel, Canada, American Mathematical Society, Providence, RI, 1996, 51–61  mathscinet  zmath

   1995
39. I. Yu. Cherdantsev, R. I. Yamilov, “Master symmetries for differential-difference equations of the Volterra type”, Physica D, 87:1–4 (1995), 140–144 , Elsevier (North-Holland), Amsterdam  crossref  mathscinet  zmath  isi (cited: 40)  scopus (cited: 41)

   1994
40. S. I. Svinolupov, R. I. Yamilov, “Explicit Bäcklund transformations for multifield Schrödinger equations. Jordan generalizations of the Toda chain”, Theoret. and Math. Phys., 98:2 (1994), 139–146  mathnet  crossref  mathscinet  zmath  isi (cited: 7)  scopus (cited: 8)
41. R. I. Yamilov, “Construction scheme for discrete Miura transformations”, J. Phys. A, Math. Gen., 27:20 (1994), 6839–6851 , IOP Publishing Ltd., Bristol, UK  crossref  mathscinet  zmath  isi (cited: 52)  scopus (cited: 53)
42. V. E. Adler, R. I. Yamilov, “Explicit auto-transformations of integrable chains”, J. Phys. A, Math. Gen., 27:2 (1994), 477–492 , IOP Publishing Ltd., Bristol, UK  crossref  mathscinet  zmath  isi (cited: 35)  scopus (cited: 33)

   1993
43. A. N. Leznov, A. B. Shabat, R. I. Yamilov, “Canonical transformations generated by shifts in nonlinear lattices”, Phys. Lett. A, 174:5–6 (1993), 397–402  crossref  mathscinet  isi (cited: 42)  scopus (cited: 43)
44. R. I. Yamilov, “On the construction of Miura type transformations by others of this kind”, Phys. Lett. A, 173:1 (1993), 53–57  crossref  mathscinet  isi (cited: 10)  scopus (cited: 10)

   1991
45. S. I. Svinolupov, R. I. Yamilov, “The multi-field Schrödinger lattices”, Phys. Lett. A, 160:6 (1991), 548–552  crossref  mathscinet  isi (cited: 32)  scopus (cited: 33)
46. A. B. Shabat, R. I. Yamilov, “Symmetries of nonlinear lattices”, Leningrad Math. J., 2:2 (1991), 377–400  mathnet  mathscinet  zmath

   1990
47. R. I. Yamilov, “Invertible changes of variables generated by Bäcklund transformations”, Theoret. and Math. Phys., 85:2 (1990), 1269–1275  mathnet  crossref  mathscinet  zmath  isi (cited: 9)  scopus (cited: 13)

   1988
48. A. V. Mikhajlov, A. B. Shabat, R. I. Yamilov, “Extension of the module of invertible transformations. Classification of integrable systems”, Commun. Math. Phys., 115:1 (1988), 1–19 , Springer, Berlin/Heidelberg  crossref  mathscinet  zmath  isi (cited: 65)  scopus (cited: 64)
49. A. B. Shabat, R. I. Yamilov, “Lattice representations of integrable systems”, Phys. Lett. A, 130:4–5 (1988), 271–275  crossref  mathscinet  isi (cited: 31)  scopus (cited: 31)

   1987
50. A. V. Mikhailov, A. B. Shabat, R. I. Yamilov, “The symmetry approach to the classification of non-linear equations. Complete lists of integrable systems”, Russian Math. Surveys, 42:4 (1987), 1–63  mathnet  crossref  mathscinet  zmath  adsnasa  isi (cited: 152)  scopus (cited: 133)
51. A. V. Mikhajlov, A. B. Shabat, R. I. Yamilov, “On extending the module of invertible transformations”, Sov. Math., Dokl., 36:1 (1987), 60–63 , American Mathematical Society, Providence, RI  zmath  isi (cited: 9)

   1983
52. S. I. Svinolupov, V. V. Sokolov, R. I. Yamilov, “On Bäcklund transformations for integrable evolution equations”, Sov. Math., Dokl., 28 (1983), 165–168 , American Mathematical Society, Providence, RI  mathscinet  zmath  isi (cited: 26)
53. S. I. Svinolupov, V. V. Sokolov, R. I. Yamilov, “On Bäcklund transformations for integrable evolution equations”, Dokl. Akad. Nauk SSSR, 271:4 (1983), 802–805  mathnet  mathscinet  zmath

   1982
54. R. I. Yamilov, “On the classification of discrete equations”, 1982, Integrable systems, Work Collect., Ufa 1982, 95-114 (1982).  zmath

   1980
55. R. I. Yamilov, “On conservation laws for the difference Korteweg-de Vries equation”, Din. Splosh. Sredy, 44 (1980), 164–173 , Russian Academy of Sciences - RAS (Rossiĭskaya Akademiya Nauk - RAN), Siberian Branch (Sibirskoe Otdelenie), Institute of Hydrodynamics named after M. A. Lavrent'eva (Institut Gidrodinamiki Im. M. A. Lavrent'eva), Novosibirsk  mathscinet  zmath

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