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.
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