Group classification of variable coefficient KdV-like equations

TL;DR

This paper performs a comprehensive group classification of variable coefficient KdV-like equations and introduces a straightforward method for constructing exact solutions via equivalence transformations.

Contribution

It provides the first exhaustive classification of KdV-like equations with time-dependent coefficients and a simple approach for deriving exact solutions.

Findings

Complete group classification of KdV-like equations with variable coefficients

A method for constructing exact solutions using equivalence transformations

Identification of symmetry properties for specific equations

Abstract

The exhaustive group classification of the class of KdV-like equations with time-dependent coefficients $u_t+uu_x+g(t)u_{xxx}+h(t)u=0$ is carried out using equivalence based approach. A simple way for the construction of exact solutions of KdV-like equations using equivalence transformations is described.