Symmetries of integro-differential equations: A survey of methods illustrated by the Benny equations (Q1610755)

The paper is devoted to the study of integro-differential equations known as the Benny equations. The first such equation appeared in long wavelength hydrodynamics of an ideal incompressible fluid of finite depth in a gravitational field. Another equation of this type yields a unique representative of a set of hierarchy of kinetic equations of Vlasov-type. Various approaches to calculating symmetry groups for Benny equations are discussed. An infinite symmetry Lie algebra is calculated for a system of such integro-differential equations on the basis of the construction of symmetry generators in the form of canonical Lie-Bäcklund operators.