New Travelling-Wave Solutions for Dodd-Bullough Equation

Abstract

A new method, which assumes $\varphi \text{'}$ with a function form of $f(e^{\varphi })$, is applied to solve the Dodd-Bullough equation ${\varphi }_{uv}=e^{\varphi }-e^{-\mathrm{2}\varphi }$ through travelling-wave transformation. A new family of explicit travelling wave solutions is derived. The proposed method works efficiently to be applied to solve other forms of Dodd-Bullough equations.