Breather soliton and cross two-soliton solutions for the fifth order Caudrey-Dodd-Gibbon (CDG) equation

Abstract

Purpose

The purpose of this paper is to reveal dynamical behavior of nonlinear wave by searching for the new breather soliton and cross two-soliton solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG) equation.

Design/methodology/approach

The authors apply bilinear form and extended homoclinic test approach to the fifth-order CDG equation.

Findings

In this paper, by using bilinear form and extended homoclinic test approach, the authors obtain new breather soliton and cross two-soliton solutions of the fifth-order CDG equation. It is shown that the extended homoclinic test approach, with the help of symbolic computation, provides an effective and powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

Research limitations/implications

The research manifests that the structures of the solution to nonlinear equations are diversified and complicated.

Originality/value

The methods used in this paper can be widely applied to the research of spatial and temporal characteristics of nonlinear equations in physics and engineering technology. These methods are also conducive for people to know objective laws and grasp the essential features of the development of the world.

Citation

Chen, H., Xu, Z. and Dai, Z. (2015), "Breather soliton and cross two-soliton solutions for the fifth order Caudrey-Dodd-Gibbon (CDG) equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 3, pp. 651-655. https://doi.org/10.1108/HFF-04-2014-0116