On a generalized variable‐coefficient Gardner equation with linear damping and dissipative terms

Abstract

Summary In this paper, a generalized variable‐coefficient Gardner equation which involves a linear damping term and a dissipative term is studied. This equation broadens out a large number of equations previously considered. The equivalence group is used to simplify the analysis of the equation. The gauging of arbitrary elements of the family allows us to perform an exhaustive study of the Lie symmetries admitted by the family. Finally, by means of the multiplier method, we classify all low‐order conservation laws of the equations that have been obtained by applying the gauging.