Application of modified extended tanh method in solving fractional order coupled wave equations

Abstract

In this paper, our purpose is to analyse the dynamical behaviour of the solitary waves of coupled wave equations, namely fractional order modified Volterra’s equations. Here, the local fractional derivative viz. beta derivative has been used and the solutions are analysed for different values of the parameter β. The fractional order modified Volterra’s equations consist of two non linear fractional partial differential equations. Fractional complex transformation has been applied to convert fractional order non linear partial differential equations into integer order non linear ordinary differential equations. The modified extended tanh method is used to find ample solitary wave solutions of fractional order modified Volterra’s equations. The solutions of modified Volterra’s equations have been given in the sense of Riccati equation. Proposed method has been utilized to pluck out periodic singular soliton and kink shape solution, which are illustrated by 2D and 3D plots.