A (2+1)-dimensional Korteweg–de Vries type equation in water waves: Lie symmetry analysis; multiple exp-function method; conservation laws

Abstract

We consider a (2+1)-dimensional Korteweg–de Vries type equation which models the shallow-water waves, surface and internal waves. In the analysis, we use the Lie symmetry method and the multiple exp-function method. Furthermore, conservation laws are computed using the multiplier method.