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Article
Publication date: 9 July 2020

Jian-Gen Liu, Yi-Ying Feng and Hong-Yi Zhang

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…

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.

Details

Engineering Computations, vol. 38 no. 2
Type: Research Article
ISSN: 0264-4401

Keywords

Open Access
Article
Publication date: 4 February 2022

Dibakar Dey and Pradip Majhi

Cotton soliton is a newly introduced notion in the field of Riemannian manifolds. The object of this article is to study the properties of this soliton on certain contact metric…

Abstract

Purpose

Cotton soliton is a newly introduced notion in the field of Riemannian manifolds. The object of this article is to study the properties of this soliton on certain contact metric manifolds.

Design/methodology/approach

The authors consider the notion of Cotton soliton on almost Kenmotsu 3-manifolds. The authors use a local basis of the manifold that helps to study this notion in terms of partial differential equations.

Findings

First the authors consider that the potential vector field is pointwise collinear with the Reeb vector field and prove a non-existence of such Cotton soliton. Next the authors assume that the potential vector field is orthogonal to the Reeb vector field. It is proved that such a Cotton soliton on a non-Kenmotsu almost Kenmotsu 3-h-manifold such that the Reeb vector field is an eigen vector of the Ricci operator is steady and the manifold is locally isometric to.

Originality/value

The results of this paper are new and interesting. Also, the Proposition 3.2 will be helpful in further study of this space.

Details

Arab Journal of Mathematical Sciences, vol. ahead-of-print no. ahead-of-print
Type: Research Article
ISSN: 1319-5166

Keywords

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