Lie Symmetry Reductions and Wave Solutions of Coupled Equal Width Wave Equation

Abstract

In the present paper, we have solved the coupled equal width wave equation by using the Lie symmetry analysis method. By applying the Lie symmetry transformation to the system of non-linear partial differential equations, we obtained the infinitesimal generators to the system and converted the system of non-linear partial differential equations into the system of non-linear ordinary differential equations. Further, the obtained system of ordinary differential equations has been solved by using the tanh method and power series method. The travelling wave solution to the coupled equal width wave equation has also been obtained. We have also found some implicit solution to the coupled equal width wave equation. The convergences of power series solutions have been shown.