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ON EXPLICIT WAVE SOLUTIONS OF THE FRACTIONAL NONLINEAR DSW SYSTEM VIA THE MODIFIED KHATER METHOD

CHEN YUE

Department of Mathematics, Faculty of Science, Jiangsu University, Jiangsu, P. R. China

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DIANCHEN LU

Department of Mathematics, Faculty of Science, Jiangsu University, Jiangsu, P. R. China

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MOSTAFA M. A. KHATER

Department of Mathematics, Faculty of Science, Jiangsu University, Jiangsu, P. R. China

Department of Mathematics, Obour Institutes, Cairo 11828, Egypt

E-mail Address: mostafa.khater2024@yahoo.com

Corresponding author.

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ABDEL-HALEEM ABDEL-ATY

Department of Physics, College of Sciences, University of Bisha, P.O. Box 344, 61922 Bisha, Saudi Arabia

Physics Department, Faculty of Science, Al-Azhar University, 71524 Assiut, Egypt

E-mail Address: amabdelaty@ub.edu.sa

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W. ALHARBI

Physics Department, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia

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, and

RAGHDA A. M. ATTIA

Department of Mathematics, Faculty of Science, Jiangsu University, Jiangsu, P. R. China

Department of Basic Science, Higher Technological Institute Campus, 10th of Ramadan, Sharqia, Egypt

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https://doi.org/10.1142/S0218348X20400344Cited by:41 (Source: Crossref)

This article is part of the issue:

Special Issue on Fractal and Fractional with Applications to Nature
Guest Editors: Abdon Atangana, Emile Franc Goufo Ndongmo, José Francisco Gómez Aguilar, Muhammad Altaf Khan and Ilknur Koca

Abstract

In this paper, the exact traveling and solitary wave solutions of the fractional nonlinear Drinfeld–Sokolov–Wilson (DSW) system are obtained by employing the modified Khater (mK) method through a new fractional derivative. This system describes the flow of shallow water. Moreover, the stability property of the obtained solutions is also investigated by using the characteristics of the Hamiltonian system. Some plots are given to show more physical properties of the suggested model. The advantage and accuracy of the applied analytical schemes are verified and explained by using Mathematica 11.3, and then a comparison between our solutions and those obtained in previous research papers with different systematic schemes is carried out.

Keywords:

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Vol. 28, No. 08

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History

Received 5 January 2020

Accepted 7 March 2020

Published: June 25, 2020

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This is an Open Access article in the “Special Issue on Fractal and Fractional with Applications to Nature” published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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ON EXPLICIT WAVE SOLUTIONS OF THE FRACTIONAL NONLINEAR DSW SYSTEM VIA THE MODIFIED KHATER METHOD

Abstract

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