# Ravil I. Yamilov

• Photo 1: V.E. Adler, R.I. Yamilov, A.B. Shabat
• Photo 2: R.I. Yamilov, D. Levi
• Leading Researcher
• D.Sci. degree (Doctor of Science)
• E-mail: RvlYamilov@matem.anrb.ru
• Research interests:
• Integrable nonlinear equations of mathematical physics: differential, discrete-differential and discrete ones
• Symmetries, conservation laws, transformations and auto-transformations of integrable equations
• Classification of integrable models, integrability tests
• Curriculum vitae:
• Date of birth: April 25, 1957
• 1981, MSc in Mathematics, Bashkirian State University, Ufa, USSR
• 1981-1984, Postgraduate course in Mathematics (supervisor: Professor A.B. Shabat), Institute of Mathematics, Ufa, USSR
• 1984-present: Researcher of Institute of Mathematics, Ufa, Russian Federation
• 1984, Ph.D. degree (Candidate of Science), Leningrad Branch of Steklov Mathematical Institute, Soviet Academy of Sciences, Leningrad, USSR, Ph.D. thesis "Discrete equations of the form $du_n/dt=F(u_{n-1}, u_n, u_{n+1})$ with infinite number of local conservation laws"
• 2000, D.Sci. degree (Doctor of Science), Institute of Mathematics, Ufa, Russian Federation, D.Sci. thesis "Symmetry approach to the classification from the standpoint of integrable differential difference equations. Transformation theory"
• Number of publications: more than 50
• Main collaborators: A.B. Shabat, D. Levi, A.V. Mikhailov, V.E. Adler, S.I. Svinolupov, P. Winternitz, V.V. Sokolov, R.N. Garifullin
• Number of citations: more than 2400* (GS: Google Scholar), more than 1000 (WS: Web of Science)
• h-index: 24* (GS), 19 (WS)
• * see Google Scholar profile
• See also Mathnet profile
• Publications:
• R. N. Garifullin, R. I. Yamilov and D. LeviClassification of five-point differential-difference equations II, J. Phys. A: Math. Theor. 51 (2018) 065204  (16 pp).
• R.N. Garifullin and R.I. Yamilov, On the integrability of a lattice equation with two continuum limits, arXiv:1708.03179
• G. Gubbiotti, C. Scimiterna and R.I. YamilovDarboux integrability of trapezoidal H4 and H6 families of lattice equations II: General SolutionsarXiv:1704.05805
• R.N. Garifullin and R.I. YamilovOn integrability of a discrete analogue of Kaup-Kupershmidt equation, Ufa Mathematical Journal 9:3 (2017)  158-164.
• G. Gubbiotti and R.I. YamilovDarboux integrability of trapezoidal H4 and H6families of lattice equations I: first integrals, J. Phys. A: Math. Theor. 50 (2017) 345205  (26pp).
• R.N. Garifullin, R.I. Yamilov and D. LeviClassification of five-point differential-difference equations, J. Phys. A: Math. Theor. 50 (2017) 125201 (27pp).
• R.N. Garifullin, R.I. Yamilov and D. LeviNon-invertible transformations of differential–difference equations, J. Phys. A: Math. Theor. 49 (2016) 37LT01 (12pp).
• R.N. Garifullin, I.T. Habibullin and R.I. YamilovPeculiar symmetry structure of some known discrete nonautonomous equations, J. Phys. A: Math. Theor. 48 (2015) 235201 (27pp).
• R.N. Garifullin and 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 (2015) 012005 (18pp).
• R.N. Garifullin, A.V. Mikhailov and R.I. Yamilov, Discrete equation on a square lattice with a nonstandard structure of generalized symmetries, Teoret. Mat. Fiz. 180:1 (2014) 17-34.
English translation:
R.N. Garifullin, A.V. Mikhailov and R.I. Yamilov, Discrete equation on a square lattice with a nonstandard structure of generalized symmetries, Theor. Math. Phys. 180:1 (2014) 765-780.
• R.N. Garifullin and R.I. Yamilov, Examples of Darboux integrable discrete equations possessing first integrals of an arbitrarily high minimal order, Ufa Mathematical Journal 4:3 (2012) 174-180.
• R.N. Garifullin and R.I. Yamilov, Generalized symmetry classification of discrete equations of a class depending on twelve parameters, J. Phys. A: Math. Theor. 45 (2012) 345205 (23pp).
Cited by 30 (GS), 13 (WS)
• D. Levi, P. Winternitz and R.I. Yamilov, Symmetries of the continuous and discrete Krichever-Novikov equation, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 7 (2011), 097, 16 pages.
• D. Levi and R.I. Yamilov, Generalized Lie symmetries for difference equations, In: Symmetries and Integrability of Difference Equations (Eds. D. Levi, P. Olver, Z. Thomova, P. Winternitz), London Mathematical Society Lecture Note series No. 381, Cambridge University Press 2011, 160-190.
http://www.cambridge.org/9780521136587
• D. Levi and R.I. Yamilov, Generalized symmetry integrability test for discrete equations on the square lattice, J. Phys. A: Math. Theor. 44 (2011) 145207 (22pp).
Included in IOP Select of IOP Publishing, 2011.
Cited by 26 (GS), 18 (WS)
• D. Levi and R.I. Yamilov, Integrability test for discrete equations via generalized symmetries, In: Symmetries in Nature: Symposium in Memoriam of Marcos Moshinsky, Cuernavaca, Mexico, 7-14 August 2010 (Eds: L. Benet, P.O. Hess, J.M. Torres, K.B. Wolf), AIP Conference Proceedings, 2010, V. 1323, 203-214.
• D. Levi, P. Winternitz and R.I. Yamilov, Lie point symmetries of differential-difference equations, J. Phys. A: Math. Theor. 43 (2010) 292002 (14pp).
• D. Levi and R.I. Yamilov, The generalized symmetry method for discrete equations, J. Phys. A: Math. Theor. 42 (2009) 454012 (18pp).
Cited by 33 (GS), 22 (WS)
• D. Levi and R.I. Yamilov, On a nonlinear integrable difference equation on the square, Ufa Mathematical Journal 1:2 (2009) 101-105.
• D. Levi, M. Petrera, C. Scimiterna and R. Yamilov, On Miura transformations and Volterra-type equations associated with the Adler-Bobenko-Suris equations, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 4 (2008), 077, 14 pages.
Cited by 27 (GS), 17 (WS)
• R.I. Yamilov, Integrability conditions for an analogue of the relativistic Toda chain, Teoret. Mat. Fiz. 151:1 (2007) 66-80.
English translation:
R.I. Yamilov, Integrability conditions for an analogue of the relativistic Toda chain, Theor. Math. Phys. 151:1 (2007) 492-504.
• R. Yamilov, Symmetries as integrability criteria for differential difference equations, J. Phys. A: Math. Gen. 39 (2006) R541-R623.
Cited by 89 (GS), 53 (WS)
Included in Mathematical Physics Featured Section of J. Phys. A, 2008.
• R.I. Yamilov, Relativistic Toda chains and Schlesinger transformations, Teoret. Mat. Fiz. 139:2 (2004) 209-224.
English translation:
R.I. Yamilov, Relativistic Toda chains and Schlesinger transformations, Theor. Math. Phys. 139:2 (2004) 623-635.
• R. Yamilov and D. Levi, Integrability conditions for n and t dependent dynamical lattice equations, J. Nonl. Math. Phys. 11:1 (2004) 75-101.
• D. Levi and R. Yamilov, On the integrability of a new discrete nonlinear Schrodinger equation, J. Phys. A: Math. Gen. 34 (2001) L553-L562.
• D. Levi and R. Yamilov, Conditions for the existence of higher symmetries and nonlinear evolutionary equations on the lattice, In: Algebraic Methods in Physics: A Symposium for the 60th Birthdays of Jiri Patera and Pavel Winternitz (Eds: Y. Saint-Aubin, L. Vinet), Springer-Verlag, 2001, 135-148.
• V.E. Adler, A.B. Shabat and R.I. Yamilov, Symmetry approach to the integrability problem, Teoret. Mat. Fiz. 125:3 (2000) 355-424.
English translation:
V.E. Adler, A.B. Shabat and R.I. Yamilov, Symmetry approach to the integrability problem, Theor. Math. Phys. 125:3 (2000) 1603-1661.
Cited by 136 (GS), 76 (WS)
• D. Levi and R. Yamilov, Non-point integrable symmetries for equations on the lattice, J. Phys. A: Math. Gen. 33 (2000) 4809-4823.
• D. Levi and R. Yamilov, Dilation symmetries and equations on the lattice, J. Phys. A: Math. Gen. 32 (1999) 8317-8323.
• V.E. Adler, S.I. Svinolupov and R.I. Yamilov, Multi-component Volterra and Toda type integrable equations, Phys. Lett. A 254 (1999) 24-36.
Cited by 84 (GS), 64 (WS)
• A.V. Mikhailov and R.I. Yamilov, Towards classification of (2+1)-dimensional integrable equations. Integrability conditions I, J. Phys. A: Math. Gen. 31 (1998) 6707-6715.
Cited by 57 (GS), 28 (WS)
• A.V. Mikhailov and R.I. Yamilov, On integrable two-dimensional generalizations of nonlinear Schrodinger type equations, Phys. Lett. A 230 (1997) 295-300.
• D. Levi and R. Yamilov, Conditions for the existence of higher symmetries of evolutionary equations on the lattice, J. Math. Phys. 38:12 (1997) 6648-6674.
Cited by 135 (GS), 91 (WS)
• A.B. Shabat and R.I. Yamilov, To a transformation theory of two-dimensional integrable systems, Phys. Lett. A 227 (1997) 15-23.
Cited by 53 (GS), 35 (WS)
• I.T. Habibullin, V.V. Sokolov and R.I. Yamilov, Multi-component integrable systems and nonassociative structures, In: Proceedings of 1st Int. Workshop on Nonlinear Physics: Theory and Experiment, Gallipoli, Italy, 29 June - 7 July 1995 (Eds: E. Alfinito, M. Boiti, L. Martina, F. Pempinelli), World Scientific Publishing, 1996, 139-168.
Cited by 24 (GS)
• I. Cherdantsev and R. Yamilov, Local master symmetries of differential-difference equations, In: Proceedings of 1st Int. Workshop on Symmetries and Integrability of Difference Equations SIDE-1, Montreal, Canada, 22-29 May 1994, Centre de Recherches Mathematiques, CRM Proceedings and Lecture Notes, 1996, V. 9, 51-61.
Symmetries and integrability of difference equations, 1996 - books.google.com
• I.Yu. Cherdantsev and R.I. Yamilov, Master symmetries for differential-difference equations of the Volterra type, Physica D 87 (1995) 140-144.
Cited by 52 (GS), 36 (WS)
• V.E. Adler and R.I. Yamilov, Explicit auto-transformations of integrable chains, J. Phys. A: Math. Gen. 27 (1994) 477-492.
Cited by 49 (GS), 30 (WS)
• S.I. Svinolupov and R.I. Yamilov, Explicit Backlund transformations for multifield Schrodinger equations. Jordan generalizations of the Toda chain, Teoret. Mat. Fiz. 98:2 (1994) 207-219.
English translation:
S.I. Svinolupov and R.I. Yamilov, Explicit Backlund transformations for multifield Schrodinger equations. Jordan generalizations of the Toda chain, Theor. Math. Phys. 98:2 (1994) 139-146.
• R.I. Yamilov, Construction scheme for discrete Miura transformations, J. Phys. A: Math. Gen. 27 (1994) 6839-6851.
Cited by 64 (GS), 50 (WS)
• R.I. Yamilov, On the construction of Miura type transformations by others of this kind, Phys. Lett. A 173 (1993) 53-57.
• A.N. Leznov, A.B. Shabat and R.I. Yamilov, Canonical transformations generated by shifts in nonlinear lattices, Phys. Lett. A 174 (1993) 397-402.
Cited by 59 (GS), 41 (WS)
• R.I. Yamilov, Generalizations of the Toda lattice, and conservation laws, Preprint, Soviet Academy of Sciences, Bashkirian Scientific Center, Institute of Mathematics, Ufa, 1989, 21 pp.
English version:
R.I. Yamilov, Classification of Toda type scalar lattices, In: Proceedings of 8th Int. Workshop on Nonlinear Evolution Equations and Dynamical Systems NEEDS'92, Dubna, Russia, 6-17 July 1992 (Eds: V. Makhankov, I. Puzynin, O. Pashaev), World Scientific Publishing, 1993, 423-431.
Cited by 44 (GS)
• S.I. Svinolupov and R.I. Yamilov, The multi-field Schrodinger lattices, Phys. Lett. A 160 (1991) 548-552.
Cited by 46 (GS), 31 (WS)
• R.A. Sharipov and R.I. Yamilov, Backlund transformation and the construction of the integrable boundary-value problem for the equation uxx -utt = eu - e-2u, In: Problems of mathematical physics and asymptotic of their solutions (Eds: V.Yu. Novokshenov, S.V. Khabirov, O.B. Sokolova), Soviet Academy of Sciences, Bashkirian Scientific Center, Institute of Mathematics, Ufa, 1991, 66-77.
arXiv:solv-int/9412001
• A.B. Shabat and R.I. Yamilov, Symmetries of nonlinear chains, Algebra i Analiz 2:2 (1990) 183-208.
English translation:
A.B. Shabat and R.I. Yamilov, Symmetries of nonlinear chains, Leningrad Math. J. 2:2 (1991) 377-400.
Cited by 185 (GS)
• R.I. Yamilov, Invertible changes of variables generated by Backlund transformations, Teoret. Mat. Fiz. 85:3 (1990) 368-375.
English translation:
R.I. Yamilov, Invertible changes of variables generated by Backlund transformations, Theor. Math. Phys. 85:3 (1991) 1269-1275.
Cited by 24 (GS), 6 (WS)
• A.B. Shabat and R.I. Yamilov, Lattice representations of integrable systems, Phys. Lett. A 130 (1988) 271-275.
Cited by 44 (GS), 28 (WS)
• A.V. Mikhailov, A.B. Shabat and R.I. Yamilov, Extension of the module of invertible transformations. Classification of integrable systems, Commun. Math. Phys. 115 (1988) 1-19.
Cited by 92 (GS), 58 (WS)
• A.V. Mikhailov, A.B. Shabat and R.I. Yamilov, On extending the module of invertible transformations, Dokl. Akad. Nauk SSSR 295:2 (1987) 288-291.
English translation:
A.V. Mikhailov, A.B. Shabat and R.I. Yamilov, On extending the module of invertible transformations, Soviet Math. Dokl. 36:1 (1988) 60-63.
• A.V. Mikhailov, A.B. Shabat and R.I. Yamilov, The symmetry approach to the classification of nonlinear equations. Complete lists of integrable systems, Uspekhi Mat. Nauk 42:4 (1987) 3-53.
English translation:
A.V. Mikhailov, A.B. Shabat and R.I. Yamilov, The symmetry approach to the classification of nonlinear equations. Complete lists of integrable systems, Russian Math. Surveys 42:4 (1987) 1-63.
Cited by 325 (GS), 135 (WS)
• S.I. Svinolupov, V.V. Sokolov and R.I. Yamilov, On Backlund transformations for integrable evolution equations, Dokl. Akad. Nauk SSSR 271:4 (1983) 802-805.
English translation:
S.I. Svinolupov, V.V. Sokolov and R.I. Yamilov, On Backlund transformations for integrable evolution equations, Soviet Math. Dokl. 28:1 (1983) 165-168.
Cited by 105 (GS)
• R.I. Yamilov, Classification of discrete evolution equations, Uspekhi Mat. Nauk 38:6 (1983) 155-156 (in Russian).
Cited by 80 (GS)
• A.B. Shabat and R.I. Yamilov, Exponential systems of the type I and the Cartan matrices, Preprint, Soviet Academy of Sciences, Bashkirian Branch, Ufa, 1981, 22 pp (in Russian).
Cited by 87 (GS)