Modified Double Sub-equation Method for Finding Complexiton Solutions to the (1 + 1) Dimensional Nonlinear Evolution Equations

Abstract

This paper reflects the execution of a reliable technique which we proposed as a modified double sub-equation method for solving nonlinear evolution equations. The proposed scheme has been successfully hardened on a very important evolution equation namely the (1 + 1)-dimensional Burger equation and the (1 + 1)-dimensional Gardner equation (or combined KdV–mKdV). As a results, we found more complexiton solutions in-terms of trigonometric, hyperbolic functions. Finally, the interaction phenomena of the achieved complexiton solutions between solitary waves and/or periodic waves are presented with in depth derivation. The outcome can be used to enhance the dynamical activities of higher dimensional nonlinear wave field areas.