Analytical Approach to Obtain Some New Traveling Wave Solutions of Coupled Systems of Nonlinear Equations

Abstract

The second order nonlinear ordinary differential equation is executed as an auxiliary equation. For illustration, a new extension of so called  method is considered to investigate the generalized Hirota-Satsuma coupled KdV equations for producing some new analytical solutions. The obtained solutions belong to hyperbolic functions, trigonometric functions and rational forms which show the wider applicability of this new extended method for handling other nonlinear evolution equations. The numerical results are also described in the figures.