Some new exact solutions for a generalized variable coefficients KdV equation

Volume 29, Issue 1, pp 1--11 http://dx.doi.org/10.22436/jmcs.029.01.01

Publication Date: August 11, 2022 Submission Date: October 18, 2021 Revision Date: May 13, 2022 Accteptance Date: June 01, 2022

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Authors

R. Rajagopalan - Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia. A. H. Abdel Kader - Department of Mathematics and Engineering Physics, Engineering Faculty, Mansoura University, Mansoura, Egypt. M. S. Abdel Latif - Department of Mathematics and Engineering Physics, Engineering Faculty, Mansoura University, Mansoura, Egypt. - Department of Mathematics, Faculty of Science, New Mansoura University, New Mansoura City, Egypt. D. Baleanu - Mathematics Department, Arts and Sciences Faculty, Cankaya University, Ankara 06530, Turkey. - Instiute of Space Sciences, Magurele-Bucharest, P. O. Box MG-23, R 76900, Romania. A. E. Sonbaty - Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia. - Department of Mathematics and Engineering Physics, Engineering Faculty, Mansoura University, Mansoura, Egypt.

Abstract

In this paper, the variable coefficients KdV equation with general power nonlinearities is proposed. Firstly, it is transformed into a generalized KdV equation with constant coefficients using a point transformation. Then, the traveling wave transformation is utilized to transform the obtained constant coefficients generalized KdV equation into a generalized ordinary differential equation. We give a classification for the obtained generalized ordinary differential equation using a suitable integrating factor. Some new solutions are obtained for the generalized KdV equation with constant coefficients. All the obtained solutions in this paper for the variable coefficients KdV equation with general power nonlinearities are new.

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Keywords

• Exact solutions
• generalized KdV equation
• traveling wave
• solitons

MSC

•  35C05
•  35C07
•  35G20
•  35Q53

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