Abstract

Symmetries of Integro-Differential Equations: Several Classical and New Illustrations

V.F.Kovalev (Institute for Mathematical Modelling RAS, Moscow, Russia); N.H.Ibragimov (Research Centre ALGA: Advances in Lie Group Analysis, Department of Health, Science and Mathematics, Blekinge Institute of Technology, Karlskrona, Sweden)

e-mail: nib@bth.se

Classical Lie group theory provides a universal tool for calculating symmetry groups for systems of differential equations. However Lie's method is not as much effective in the case of integral or integro-differential equations as well as in the case of infinite systems of differential equations. This report is aimed to describe several modern approaches to symmetries of integro-differential equations. As an illustration we present new results including an infinite symmetry Lie algebra for the well-known Benny equations and a symmetry of Vlasov-Maxwell equations for quasi-neutral plasma. The crucial idea is to look for symmetry generators in the form of canonical Lie-Backlund operators.

Section : 12