Exploration of the algebraic traveling wave solutions of a higher order model. Issue 2 (9th July 2020)

• Record Type: Journal Article
• Authors: Liu, Jian-Gen; Feng, Yi-Ying; Zhang, Hong-Yi
• Is Part Of: Engineering computations. Volume 38:Issue 2(2021)
• Page Start: 618
• Page End: 631
• Publication Date: 2020-07-09
• Subjects: (3+1)-dimensional modified KdV-Z-K equation -- Algebraic traveling wave solutions -- Rational solutions; 35Q51 -- 35Q53 -- 00A05 -- 00A69 -- 35G25; Computer-aided engineering -- Periodicals; Computer graphics -- Periodicals; 620.00285
• DOI: 10.1108/EC-07-2019-0303
• Languages: English
• ISSNs: 0264-4401

Abstract

Abstract : Purpose: The purpose of this paper is to construct the algebraic traveling wave solutions of the (3 + 1)-dimensional modified KdV-Zakharov-Kuznetsve (KdV-Z-K) equation, which can be usually used to express shallow water wave phenomena. Design/methodology/approach: The authors apply the planar dynamical systems and invariant algebraic cure approach to find the algebraic traveling wave solutions and rational solutions of the (3 + 1)-dimensional modified KdV-Z-K equation. Also, the planar dynamical systems and invariant algebraic cure approach is applied to considered equation for finding algebraic traveling wave solutions. Findings: As a result, the authors can find that the integral constant is zero and non-zero, the algebraic traveling wave solutions have different evolutionary processes. These results help to better reveal the evolutionary mechanism of shallow water wave phenomena and find internal connections. Research limitations/implications: The paper presents that the implemented methods as a powerful mathematical tool deal with (3 + 1)-dimensional modified KdV-Z-K equation by using the planar dynamical systems and invariant algebraic cure. Practical implications: By considering important characteristics of algebraic traveling wave solutions, one can understand the evolutionary mechanism of shallow water wave phenomena and find internal connections. Originality/value: To the best of the authors' knowledge, the algebraic traveling wave solutions have not been reported in other places. Finally, the algebraic traveling wave solutions nonlinear dynamics behavior was shown.