Lie symmetry analysis, exact solutions, optimal system and conservation laws for variable-coefficients Kundu–Mukherjee–Nasker equation

Abstract

This paper investigates the (2+1)-dimensional variable coefficients Kundu–Mukherjee–Nasker equation which obtained by some transformations. The infinitesimal generators of the equation are obtained by the Lie group method. Next, the representative elements of the one-dimensional subalgebras optimal system are determined with adjoint representation. Based on the optimal system, (1+1)-dimensional partial differential equations can be obtained by similarity reductions. With the help of [Formula: see text]-expansion method, several exact solutions including hyperbolic function solutions, trigonometric function solutions and rational function solutions of variable coefficients Kundu–Mukherjee–Nasker equation are obtained. Finally, the conservation laws of the variable coefficients Kundu–Mukherjee–Nasker equation can be obtained by using the conservation theorem proposed by Ibragimov.