Exact solutions via equivalence transformations of variable-coefficient fifth-order KdV equations

Abstract

In this paper, a family of variable-coefficient fifth-order KdV equations has been considered. By using an infinitesimal method based on the determination of the equivalence group, differential invariants and invariant equations are obtained. Invariants provide an alternative way to find equations from the family which may be equivalent to a specific subclass of the same family and the invertible transformation which maps both equivalent equations. Here, differential invariants are applied to obtain exact solutions.