Solitary and periodic wave solutions of(2+1)-dimensions of dispersive long wave equations on shallow waters

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.