New multi-soliton solutions and travelling wave solutions of the dispersive long-wave equations

Abstract

Using the extended homogeneous balance method, the (1+1)-dimensional dispersive long-wave equations have been solved. Starting from the homogeneous balance method, we have obtained a nonlinear transformation for simplifying a dispersive long-wave equation into a linear partial differential equation. Usually, we can obtain only a type of soliton-like solution. In this paper, we have further found some new multi-soliton solutions and exact travelling solutions of the dispersive long-wave equations from the linear partial equation.