Some new exact solutions for a generalized variable coefficients KdV equation
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, MagureleBucharest, P. O. Box MG23, 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.
Share and Cite
ISRP Style
R. Rajagopalan, A. H. Abdel Kader, M. S. Abdel Latif, D. Baleanu, A. E. Sonbaty, Some new exact solutions for a generalized variable coefficients KdV equation, Journal of Mathematics and Computer Science, 29 (2023), no. 1, 111
AMA Style
Rajagopalan R., Abdel Kader A. H., Abdel Latif M. S., Baleanu D., Sonbaty A. E., Some new exact solutions for a generalized variable coefficients KdV equation. J Math Comput SCIJM. (2023); 29(1):111
Chicago/Turabian Style
Rajagopalan, R., Abdel Kader, A. H., Abdel Latif, M. S., Baleanu, D., Sonbaty, A. E.. "Some new exact solutions for a generalized variable coefficients KdV equation." Journal of Mathematics and Computer Science, 29, no. 1 (2023): 111
Keywords
 Exact solutions
 generalized KdV equation
 traveling wave
 solitons
MSC
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