Speciality:
01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
25.04.1957
Website: https://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:
D. Levi, R. I. Yamilov, “The generalized symmetry method for discrete equations”, J. Phys. A, Math. Theor., 42:45 (2009), 18 , IOP Publishing, Bristol
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
V. E. Adler, A. B. Shabat, R. I. Yamilov, “Symmetry approach to the integrability problem”, Theoret. and Math. Phys., 125:3 (2000), 1603–1661
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
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
