Algorithms and Some New Traveling Wave Solutions via New Extension of (G'/G) -expansion Method of Coupled Nonlinear Equations

In this work, the second order nonlinear ordinary differential equation is implemented as an auxiliary equation. For illustration, the generalized Hirota-Satsuma coupled KdV equations are considered for constructing traveling wave solutions by applying a new extension of so called (G'/G) method. As a result, many new traveling wave solutions have been generated with many arbitrary parameters. The obtained solutions also show the wider applicability of this new extended method for handling nonlinear evolution equations. The numerical results are also described in the figures.