Solitary Wave Solutions of the coupled Kawahara Equation

Abstract

The field of nonlinear differential equations have made significant contribution in understanding nonlinear dynamics and its complex phenomenon. One such evolution equation is Kawahara equation, which has gained its importance in plasma physics and allied fields. Many researchers are interested to work on their soliton, multi-solitons solutions and to study other properties such as stability, integrability, conservation laws and so on. The aim of the paper is to study the Coupled Kawahara equation and to deduce its soliton solutions. The coupled equation is treated with the ansatz method and the tanh method to compute soliton solutions. The novelty of this work is to demonstrate the fact, that the derived system efficiently gives two governing equations admitting solitary wave solutions. Further, in the coupled equation, one equation has the nonlinear term vv_x addition to the Kawahara equation, while the other is the modified Kawahara equation. Scope for future works is also highlighted.