Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches

Ibrahim Alraddadi; Faisal Alsharif; Sandeep Malik; Hijaz Ahmad; Taha Radwan; Karim K. Ahmed; Ibrahim Alraddadi; Faisal Alsharif; Sandeep Malik; Hijaz Ahmad; Taha Radwan; Karim K. Ahmed

doi:10.3934/math.20241664

AIMS Mathematics

2024, Volume 9, Issue 12: 34966-34980. doi: 10.3934/math.20241664

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Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches

1.
Department of Mathematics, Faculty of Science, Islamic University of Madinah, Madinah, Saudi Arabia
2.
Department of Mathematics, College of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
3.
Department of Mathematics, Akal University, Talwandi Sabo, Bathinda, Punjab, 151302, India
4.
Operational Research Center in Healthcare, Near East University, Nicosia/TRNC, 99138 Mersin 10, Turkey
5.
Department of Technical Sciences, Western Caspian University, Baku, 1001, Azerbaijan
6.
Department of Management Information Systems, College of Business and Economics, Qassim University, Buraydah 51452, Saudi Arabia
7.
Department of Mathematics, Faculty of Engineering, German International University (GIU), New Administrative Capital, Cairo, Egypt

Received: 08 August 2024 Revised: 28 November 2024 Accepted: 04 December 2024 Published: 16 December 2024
MSC : 35B35, 35C07, 35C08, 35C09

In this paper, we analyze and provide innovative soliton solutions for a (2+1)-dimensional generalized Korteweg-de Vries (gKdV) problem. We obtain phase shifts and dispersion relations by using the generalized Arnous technique and the Riccati equation approach, thus allowing different soliton solutions to be developed. Several precise solutions with special structural properties, including kink and solitary soliton solutions, are included in our study. This detailed examination demonstrates the complex behavior of the model and its capability to explain a large scale of nonlinear wave occurrences in many physical settings. Thus, in scientific domains such as fluid mechanics, plasma physics, and wave propagation in media ranging from ocean surfaces to optical fibers, our results are crucial to comprehend the principles behind the production and propagation of many complicated phenomena. Finally, we provide 2D and 3D graphs for various solutions that have been obtained using Maple.
- mathematical model,
- analytic solutions,
- soliton solutions,
- generalized KdV equation,
- generalized Arnous method,
- Riccati equation method
Citation: Ibrahim Alraddadi, Faisal Alsharif, Sandeep Malik, Hijaz Ahmad, Taha Radwan, Karim K. Ahmed. Innovative soliton solutions for a (2+1)-dimensional generalized KdV equation using two effective approaches[J]. AIMS Mathematics, 2024, 9(12): 34966-34980. doi: 10.3934/math.20241664

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Abstract

In this paper, we analyze and provide innovative soliton solutions for a (2+1)-dimensional generalized Korteweg-de Vries (gKdV) problem. We obtain phase shifts and dispersion relations by using the generalized Arnous technique and the Riccati equation approach, thus allowing different soliton solutions to be developed. Several precise solutions with special structural properties, including kink and solitary soliton solutions, are included in our study. This detailed examination demonstrates the complex behavior of the model and its capability to explain a large scale of nonlinear wave occurrences in many physical settings. Thus, in scientific domains such as fluid mechanics, plasma physics, and wave propagation in media ranging from ocean surfaces to optical fibers, our results are crucial to comprehend the principles behind the production and propagation of many complicated phenomena. Finally, we provide 2D and 3D graphs for various solutions that have been obtained using Maple.

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