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New approach for soliton solutions for the (2 + 1)-dimensional KdV equation describing shallow water wave

Suheil Khuri (Department of Mathematics and Statistics, American University of Sharjah, Sharjah, United Arab Emirates)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 1 November 2022

Issue publication date: 20 January 2023

129

Abstract

Purpose

The purpose of this study is to produce families of exact soliton solutions (2+1)-dimensional Korteweg-de Vries (KdV) equation, that describes shallow water waves, using an ansätze approach.

Design/methodology/approach

This article aims to introduce a recently developed ansätze for creating soliton and travelling wave solutions to nonlinear nonintegrable partial differential equations, especially those with physical significance.

Findings

A recently developed ansätze solution was used to successfully construct soliton solutions to the (2 + 1)-dimensional KdV equation. This straightforward method is an alternative to the Painleve test analysis, yielding similar results. The strategy demonstrated the existence of a single soliton solution, also known as a localized wave or bright soliton, as well as singular solutions or kink solitons.

Originality/value

The ansätze solution used to construct soliton solutions to the (2 + 1)-dimensional KdV equation is novel. New soliton solutions were also obtained.

Keywords

Acknowledgements

The author declares that no funds, grants or other support were received during the preparation of this manuscript.

The author has no relevant financial or nonfinancial interests to disclose.

Data Availability: Data sharing was not applicable to this paper as no data sets were generated or analyzed during the current study.

Citation

Khuri, S. (2023), "New approach for soliton solutions for the (2 + 1)-dimensional KdV equation describing shallow water wave", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 33 No. 3, pp. 965-973. https://doi.org/10.1108/HFF-08-2022-0498

Publisher

:

Emerald Publishing Limited

Copyright © 2022, Emerald Publishing Limited

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