SOLITONS AND OTHER SOLUTIONS TO NONLINEAR PDEs

Abstract

In this article, we apply \(\left(\frac{G}{G^{’}}\right)\)-expansion method to construct exact traveling wave solutions with parameters of four nonlinear PDEs having non-integer balance numbers, namely, the convection-diffusion-reaction equation with power-law nonlinearity with density-independent (or density-dependent) diffusion, and the generalized KdV-mKdV equation with any order (or with higher-order) nonlinear terms.  When the parameters take up special values, the solitary wave solutions as well as the trigonometric and rational function solutions are derived from the exact traveling wave solutions.  The used method in this article presents a wider applicability for handling nonlinear wave equations.