Symmetries of Integro-Differential Equations: A Survey of Methods Illustrated by the Benney Equations

Details Symmetries of Integro-Differential Equations: A Survey of Methods Illustrated by the Benney Equations Symmetries of Integro-Differential Equations: A Survey of Methods Illustrated by the Benney Equations

2001-09-14

arxiv.org/abs/math-ph/0109012v2

Nonlinear Dynamics, 28(2) (2002) 135-153

Physics

Mathematical Physics

Latex2e, 21 pages, typos corrected

Scientific paper

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 paper is aimed to survey the modern approaches to symmetries of integro-differential equations. As an illustration, an infinite symmetry Lie algebra is calculated for a system of integro-differential equations, namely the well-known Benney equations. The crucial idea is to look for symmetry generators in the form of canonical Lie-Backlund operators.

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