Solitons and other solutions of the long-short wave equation

Ghodrat Ebadi (Department of Mathematical Sciences, University of Tabriz, Tabriz, Iran)
Aida Mojaver (Department of Mathematical Sciences, University of Tabriz, Tabriz, Iran)
Sachin Kumar (School of Mathematics and Computer Applications, Thapar University, Patiala, India)
Anjan Biswas (Department of Mathematical Sciences, Delaware State University, Dover, Delaware, USA and Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 5 January 2015

Abstract

Purpose

The purpose of this paper is to discuss the integrability studies to the long-short wave equation that is studied in the context of shallow water waves. There are several integration tools that are applied to obtain the soliton and other solutions to the equation. The integration techniques are traveling waves, exp-function method, G′/G-expansion method and several others.

Design/methodology/approach

The design of the paper is structured with an introduction to the model. First the traveling wave hypothesis approach leads to the waves of permanent form. This eventually leads to the formulation of other approaches that conforms to the expected results.

Findings

The findings are a spectrum of solutions that lead to the clearer understanding of the physical phenomena of long-short waves. There are several constraint conditions that fall out naturally from the solutions. These poses the restrictions for the existence of the soliton solutions.

Originality/value

The results are new and are sharp with Lie symmetry analysis and other advanced integration techniques in place. These lead to the connection between these integration approaches.

Keywords

Citation

Ebadi, G., Mojaver, A., Kumar, S. and Biswas, A. (2015), "Solitons and other solutions of the long-short wave equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 25 No. 1, pp. 129-145. https://doi.org/10.1108/HFF-07-2013-0233

Publisher

:

Emerald Group Publishing Limited

Copyright © 2015, Emerald Group Publishing Limited

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