**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

- 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

- 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"

**Publications:**- G. Gubbiotti, C. Scimiterna and R.I. Yamilov,
*Darboux integrability of trapezoidal H*, SIGMA 14 (^{4}and H^{6}families of lattice equations II: General Solutions**2018**), 008, 51 pages. - R. N. Garifullin, R. I. Yamilov and D. Levi,
*Classification 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 - R.N. Garifullin and R.I. Yamilov,
*On integrability of a discrete analogue of*, Ufa Mathematical Journal 9:3 (*Kaup-Kupershmidt equation***2017**) 158-164. **G. Gubbiotti and R.I. Yamilov,***Darboux integrability of trapezoidal H*, J. Phys. A: Math. Theor. 50 (^{4}and H^{6}families of lattice equations I: first integrals**2017**) 345205 (26pp).- R.N. Garifullin, R.I. Yamilov and D. Levi,
*Classification of five-point differential-difference equations*, J. Phys. A: Math. Theor. 50 (**2017**) 125201 (27pp). - R.N. Garifullin, R.I. Yamilov and D. Levi,
*Non-invertible transformations of differential–difference equations*, J. Phys. A: Math. Theor. 49 (**2016**) 37LT01 (12pp). - R.N. Garifullin, I.T. Habibullin and R.I. Yamilov,
*Peculiar 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**38**(GS),**24**(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**35****22**(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**43****26**(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**32****20**(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**112**(GS),**73**(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**150****85**(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**89****65**(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**60****32**(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**142****98**(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**58****37**(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**27** - 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**55****37**(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**51****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**65****52**(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**61****42**(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**45** - S.I. Svinolupov and R.I. Yamilov,
*The multi-field Schrodinger lattices*, Phys. Lett. A 160 (**1991**) 548-552.

Cited by**49****32**(WS) - R.A. Sharipov and R.I. Yamilov,
*Backlund transformation and the construction of the integrable boundary-value problem for the equation*u_{xx }-u_{tt }= e^{u}- 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**190** - 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****6**(WS) - A.B. Shabat and R.I. Yamilov,
*Lattice representations of integrable systems*, Phys. Lett. A 130 (**1988**) 271-275.

Cited by**45****30**(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**100****60**(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**346****142**(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**112****26**(WS) - R.I. Yamilov,
*Classification of discrete evolution equations*, Uspekhi Mat. Nauk 38:6 (**1983**) 155-156 (in Russian).

Cited by**94** - 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**92**