Symmetries of IntegroDifferential Equations: A Survey of Methods Illustrated by the Benney Equations
Abstract
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 integrodifferential 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 integrodifferential equations. As an illustration, an infinite symmetry Lie algebra is calculated for a system of integrodifferential equations, namely the wellknown Benney equations. The crucial idea is to look for symmetry generators in the form of canonical LieBacklund operators.
 Publication:

arXiv eprints
 Pub Date:
 September 2001
 arXiv:
 arXiv:mathph/0109012
 Bibcode:
 2001math.ph...9012I
 Keywords:

 Mathematical Physics;
 Mathematics  Mathematical Physics;
 45K05;
 70Gxx:70G65;
 76Mxx:76M60
 EPrint:
 Latex2e, 21 pages, typos corrected