Modified (G′/G)-expansion method for finding traveling wave solutions of the coupled Benjamin–Bona–Mahony-KdV equation

Abstract

Using the Lie symmetry approach, the author has examined traveling wave solutions of coupled Benjamin–Bona–Mahony-KdV equation. The coupled Benjamin–Bona–Mahony-KdV equation is reduced to nonlinear ordinary differential equations for all optimal subalgebras by using Lie classical symmetries and various solutions are obtained by the modified (G′/G)-expansion method. Further, with the aid of solutions of the nonlinear ordinary differential equations, more explicit traveling wave solutions of the coupled Benjamin–Bona–Mahony-KdV equation are found out. The traveling wave solutions are expressed by rational function.