On symmetry group properties of the Benney equations
Abstract:
In the present study, we investigate the symmetry groups of Benney
equations that are the system of integro-differential equations. We first
investigate the symmetry groups of the Benney equations by using the method
that will be explained in the study. Then we obtain all reduced forms of
the system of integro-differential equations with fewer variables based
on symmetry groups; and lastly, we seek some similarity solutions to the
reduced system of the equations. It is shown that one may transform the
solution of the reduced forms into nonlinear shallow-water equations and
Benney equations derived from two-dimensional Euler equations for inviscid
and incompressible fluid.
Keywords: Benney equations; integro-differential equations; Lie groups; similarity solutions.