Abstract
•The Lie symmetry method has been implemented for getting similarity reduction for the (2+1)-dimensions of ispersive long wave equations on shallow waters.•The system of ordinary differential equations are investigated.•The exact solutions of equations utilized by the general Kudryashov method.•Some figures are given to show the properties of the solutions.
In this investigation, the (2+1)-dimensions of dispersive long wave equations on shallow waters which are called Wu-Zhang (WZ) equations are studied by using symmetry analysis. The system of partial differential equations are reduced to the type of system of ordinary differential equations. The exact solutions of ordinary differential equations are obtained by the general Kudryashov method [2]. Exact solutions including singular wave, kink wave and anti-kink wave are shown. Some figures are given to show the properties of the solutions.