Bifurcations of traveling wave solutions for Dodd–Bullough–Mikhailov equation and coupled Higgs equation and their applications

Abstract

In this article, we shall introduce a new and more general traveling wave solutions for Dodd–Bullough–Mikhailov equation and coupled Higgs equation according to the modified extended tanh-function method with the aid of Maple 16. The important fact of this method is to explain the solitary wave solutions for nonlinear partial differential equations (NLPDEs.) which illustrate the physical phenomena and help other researchers for investigating the stability of Dodd–Bullough–Mikhailov equation and coupled Higgs equation. The traveling wave solutions; solitary wave solutions; dark and bell soliton solutions of nonlinear Dodd–Bullough–Mikhailov and coupled Higgs dynamical equations are constructed by employing modified extended tanh method, which have important applications in applied mathematics and physics. Furthermore, we also present the formation conditions of the traveling wave solutions; solitary wave solutions; dark and bell soliton solutions for these equations. Comparison between our results and the well-known results will be presented.