INSTITUTE OF MATHEMATICS


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Depart ment of Mathematical Physics

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Scientific Interests
Experience
Conferences
Publications

About the Department

Ravil Islamovich Yamilov

Leading Researcher,
Doctor of Science

RvlYamilov@matem.anrb.ru

Scientific Interests

  • Classification methods of integrable nonlinear equations of mathematical physics

  • Integrability test for equations

  • Transformations and auto-transformations of integrable equations

Experience

  • 1981 Mathematician diploma, Bashkir State University, Ufa
  • Since 1984 work in the Institute of Mathematics, Ufa Scientific Center of RAS
  • 2000 Doctor's degree, Institute of Mathematics, Ufa Scientific Center of RAS

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Conferences

  • February 4-6, 2005: Rome, Italy, Workshop for Francesco Calogero 70th birthday on Solitons, Boomerons and Isochronous Solutions to Nonlinear Systems.
  • May 26-31, 2003: Montreal, Canada, Int. Workshop on Group Theory and Numerical Analysis.
  • July 26 - August 6, 1999: Montreal, Canada, 38th Session of `Seminaire de Mathematiques Superieures' on Integrable Systems: from Classical to Quantum.
  • December 15-21, 1996: Torino, Italy, Int. Workshop on Symmetry and Perturbation Theory.
  • June 29 - July 7, 1995: Gallipoli, Italy, Int. Workshop on Nonlinear Physics: Theory and Experiment.
  • July 25 - August 3, 1994: Chernogolovka, Russia, Int. Workshop on Nonlinear Schrodinger Equation: Achievements, Developments, Perspectives.
  • May 22-29, 1994: Montreal, Canada, 1st Int. Workshop on Symmetries and Integrability of Difference Equations.
  • September 3-12, 1993: Gallipoli, Italy, 9th Int. Workshop on Nonlinear Evolution Equations and Dynamical Systems.
  • July 6-17, 1992: Dubna, Russia, 8th Int. Workshop on Nonlinear Evolution Equations and Dynamical Systems.

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Publications

  • 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).
  • D. Levi and R.I. Yamilov, On a nonlinear integrable difference equation on the square, Ufa Math. J. 1:2 (2009) 101-105. (arXiv:0902.2126v2)
  • 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.
  • R.I. Yamilov, Integrability conditions for an analogue of the relativistic Toda chain, Theor. Math. Phys. 151:1 (2007) 492-504. [TMP_Y07.pdf]
  • R. Yamilov, Symmetries as integrability criteria for differential difference equations, J. Phys. A: Math. Gen. 39 (2006) R541-R623. [JPA_Y06.pdf]
  • R.I. Yamilov, Relativistic Toda chains and Schlesinger transformations, Theor. Math. Phys. 139:2 (2004) 623-635. [TMP_Y04.pdf]
  • R. Yamilov and D. Levi, Integrability conditions for $n$ and $t$ dependent dynamical lattice equations, J. Nonl. Math. Phys. 11:1 (2004) 75-101. [JNMP_LY04.pdf]
  • D. Levi and R. Yamilov, On the integrability of a new discrete nonlinear Schrodinger equation, J. Phys. A: Math. Gen. 34 (2001) L553-L562. [JPA_LY01.pdf]
  • 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, Theor. Math. Phys. 125:3 (2000) 355-424. [in Russian] [TMF_ASY00.ps]
    English transl.: V.E. Adler, A.B. Shabat and R.I. Yamilov, Symmetry approach to the integrability problem, Theor. Math. Phys. 125:3 (2000) 1603-1661. [TMP_ASY00.pdf]
  • D. Levi and R. Yamilov, Non-point integrable symmetries for equations on the lattice, J. Phys. A: Math. Gen. 33 (2000) 4809-4823. [JPA_LY00.pdf]
  • D. Levi and R. Yamilov, Dilation symmetries and equations on the lattice, J. Phys. A: Math. Gen. 32 (1999) 8317-8323. [JPA_LY99.pdf]
  • 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. [PLA_ASvY99.pdf]
  • 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. [JPA_MY98.pdf]
  • 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.
  • A.B. Shabat and R.I. Yamilov, To a transformation theory of two-dimensional integrable systems, Phys. Lett. A 227 (1997) 15-23.
  • 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.
  • I.Yu. Cherdantsev and R.I. Yamilov, Master symmetries for differential-difference equations of the Volterra type, Physica D 87 (1995) 140-144. [PhD_CY95.pdf]
  • 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, Vol. 9, 1996, 51-61. (Symmetries and integrability of difference equations, 1996 - books.google.com)
  • V.E. Adler and R.I. Yamilov, Explicit auto-transformations of integrable chains, J. Phys. A: Math. Gen. 27 (1994) 477-492. [JPA_AY94.pdf]
  • 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) 207-219. [in Russian]
    English transl.: 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. [JPA_Y94.pdf]
  • 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.
  • S.I. Svinolupov and R.I. Yamilov, The multi-field Schrodinger lattices, Phys. Lett. A 160 (1991) 548-552.
  • 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/9412001v1
  • A.B. Shabat and R.I. Yamilov, Symmetries of nonlinear chains, Algebra i Analiz 2:2 (1990) 183-208 [in Russian]
    English transl.: A.B. Shabat and R.I. Yamilov, Symmetries of nonlinear chains, Leningrad Math. J. 2:2 (1991) 377-400.
  • R.I. Yamilov, Invertible changes of variables generated by Backlund transformations, Theor. Math. Phys. 85:3 (1990) 368-375.[in Russian]
    English transl.: R.I. Yamilov, Invertible changes of variables generated by Backlund transformations, Theor. Math. Phys. 85:3 (1991) 1269-1275.
  • R.I. Yamilov, Generalizations of the Toda lattice, and conservation laws, Preprint, Soviet Academy of Sciences, Bashkirian Scientific Center, Institute of Mathematics, Ufa, 1989 [in Russian]
    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.
  • A.B. Shabat and R.I. Yamilov, Lattice representations of integrable systems, Phys. Lett. A 130 (1988) 271-275.
  • 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.
  • 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 (1887) 3-53 [in Russian]
    English transl.: 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.
  • 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 [in Russian]
    English transl.: 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.
  • 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. [in Russian]
    English transl.: 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.
  • R.I. Yamilov, Classification of discrete evolution equations, Uspekhi Mat. Nauk 38:6 (1983) 155-156 [in Russian]
  • A.B. Shabat and R.I. Yamilov, Exponential systems of the type I, and Cartan matrices, Preprint, Soviet Academy of Sciences, Bashkirian Branch, Ufa, 1981 [in Russian].

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R.I. Yamilov