Reliable analysis for obtaining exact soliton solutions of (2+1)-dimensional Chaffee-Infante equation

Naveed Iqbal; Muhammad Bilal Riaz; Meshari Alesemi; Taher S. Hassan; Ali M. Mahnashi; Ahmad Shafee; Naveed Iqbal; Muhammad Bilal Riaz; Meshari Alesemi; Taher S. Hassan; Ali M. Mahnashi; Ahmad Shafee

doi:10.3934/math.2024808

AIMS Mathematics

2024, Volume 9, Issue 6: 16666-16686. doi: 10.3934/math.2024808

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Reliable analysis for obtaining exact soliton solutions of (2+1)-dimensional Chaffee-Infante equation

1.
Deparment of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
2.
IT4Innovations, VSB-Technical University of Ostrava, Ostrava, Czech Republic
3.
Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
4.
Department of Mathematics, College of Science, University of Bisha, P.O. Box 511, Bisha 61922, Saudi Arabia
5.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, 35516, Egypt
6.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele Ⅱ, 39, 00186 Roma, Italy
7.
Department of Mathematics, Faculty of Science, Jazan University, P.O. Box 2097, Jazan 45142, Kingdom of Saudi Arabia
8.
PAAET, College of Technological Studies, Laboratory Technology Department, Shuwaikh 70654, Kuwait

Received: 08 March 2024 Revised: 23 April 2024 Accepted: 30 April 2024 Published: 14 May 2024
MSC : 34G20, 35A20, 35A22, 35R11

The (2+1)-dimensional Chaffee-Infante equation (CIE) is a significant model of the ion-acoustic waves in plasma. The primary objective of this paper was to establish and examine closed-form soliton solutions to the CIE using the modified extended direct algebraic method (m-EDAM), a mathematical technique. By using a variable transformation to convert CIE into a nonlinear ordinary differential equation (NODE), which was then reduced to a system of nonlinear algebraic equations with the assumption of a closed-form solution, the strategic m-EDAM was implemented. When the resulting problem was solved using the Maple tool, many soliton solutions in the shapes of rational, exponential, trigonometric, and hyperbolic functions were produced. By using illustrated 3D and density plots to evaluate several soliton solutions for the provided definite values of the parameters, it was possible to determine if the soliton solutions produced for CIE are cuspon or kink solitons. Additionally, it has been shown that the m-EDAM is a robust, useful, and user-friendly instrument that provides extra generic wave solutions for nonlinear models in mathematical physics and engineering.
- nonlinear partial differential equations,
- (2+1)-dimensional Chaffee-Infante equation,
- modified extended direct algebraic method,
- kink soliton,
- cuspons
Citation: Naveed Iqbal, Muhammad Bilal Riaz, Meshari Alesemi, Taher S. Hassan, Ali M. Mahnashi, Ahmad Shafee. Reliable analysis for obtaining exact soliton solutions of (2+1)-dimensional Chaffee-Infante equation[J]. AIMS Mathematics, 2024, 9(6): 16666-16686. doi: 10.3934/math.2024808

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Abstract

The (2+1)-dimensional Chaffee-Infante equation (CIE) is a significant model of the ion-acoustic waves in plasma. The primary objective of this paper was to establish and examine closed-form soliton solutions to the CIE using the modified extended direct algebraic method (m-EDAM), a mathematical technique. By using a variable transformation to convert CIE into a nonlinear ordinary differential equation (NODE), which was then reduced to a system of nonlinear algebraic equations with the assumption of a closed-form solution, the strategic m-EDAM was implemented. When the resulting problem was solved using the Maple tool, many soliton solutions in the shapes of rational, exponential, trigonometric, and hyperbolic functions were produced. By using illustrated 3D and density plots to evaluate several soliton solutions for the provided definite values of the parameters, it was possible to determine if the soliton solutions produced for CIE are cuspon or kink solitons. Additionally, it has been shown that the m-EDAM is a robust, useful, and user-friendly instrument that provides extra generic wave solutions for nonlinear models in mathematical physics and engineering.

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