Non-traveling wave solutions for the (2+1)-D Caudrey-Dodd-Gibbon-Kotera-Sawada equation

Abstract

Purpose

The purpose of this paper is to find new non-traveling wave solutions and study its localized structure of Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation.

Design/methodology/approach

The authors apply the Lie group method twice and combine with the Exp-function method and Riccati equation mapping method to the (2+1)-dimensional CDGKS equation.

Findings

The authors have obtained some new non-traveling wave solutions with two arbitrary functions of time variable.

Research limitations/implications

As non-linear evolution equations is characterized by rich dynamical behavior, the authors just found some of them and others still to be found.

Originality/value

These results may help the authors to investigate some new localized structure and the interaction of waves in high-dimensional models. The new non-traveling wave solutions with two arbitrary functions of time variable are obtained for CDGKS equation using Lie group approach twice and combining with the Exp-function method and Riccati equation mapping method by the aid of Maple.

Citation

Kang, X.-r., Daquan, X. and Dai, Z. (2015), "Non-traveling wave solutions for the (2+1)-D Caudrey-Dodd-Gibbon-Kotera-Sawada equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 3, pp. 617-628. https://doi.org/10.1108/HFF-03-2013-0086