Exploring analytical results for (2+1) dimensional breaking soliton equation and stochastic fractional Broer-Kaup system

Faeza Lafta Hasan; Mohamed A. Abdoon; Rania Saadeh; Ahmad Qazza; Dalal Khalid Almutairi; Faeza Lafta Hasan; Mohamed A. Abdoon; Rania Saadeh; Ahmad Qazza; Dalal Khalid Almutairi

doi:10.3934/math.2024570

AIMS Mathematics

2024, Volume 9, Issue 5: 11622-11643. doi: 10.3934/math.2024570

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Research article

Exploring analytical results for (2+1) dimensional breaking soliton equation and stochastic fractional Broer-Kaup system

1.
Department of Mathematics, Faculty of Education for Pure Science, Basrah University, Basrah 61001, Iraq
2.
Department of Basic Sciences, Common First Year Deanship, King Saud University, Riyadh 12373, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Bakht Al-Ruda University, Duwaym, Sudan
4.
Department of Mathematics, Faculty of Science, Zarqa University, Zarqa 13110, Jordan
5.
Department of Mathematics, College of Science Al-Zulfi, Majmaah University, Al-Majmaah 11952, Saudi Arabia

Received: 04 February 2024 Revised: 13 March 2024 Accepted: 14 March 2024 Published: 25 March 2024
MSC : 34A05, 35C08, 60G22

This paper introduces a pioneering exploration of the stochastic (2+1) dimensional breaking soliton equation (SBSE) and the stochastic fractional Broer-Kaup system (SFBK), employing the first integral method to uncover explicit solutions, including trigonometric, exponential, hyperbolic, and solitary wave solutions. Despite the extensive application of the Broer-Kaup model in tsunami wave analysis and plasma physics, existing literature has largely overlooked the complexity introduced by stochastic elements and fractional dimensions. Our study fills this critical gap by extending the traditional Broer-Kaup equations through the lens of stochastic forces, thereby offering a more comprehensive framework for analyzing hydrodynamic wave models. The novelty of our approach lies in the detailed investigation of the SBSE and SFBK equations, providing new insights into the behavior of shallow water waves under the influence of randomness. This work not only advances theoretical understanding but also enhances practical analysis capabilities by illustrating the effects of noise on wave propagation. Utilizing MATLAB for visual representation, we demonstrate the efficiency and flexibility of our method in addressing these sophisticated physical processes. The analytical solutions derived here mark a significant departure from previous findings, contributing novel perspectives to the field and paving the way for future research into complex wave dynamics.
- stochastic breaking soliton equation,
- stochastic fractional Broer-Kaup equations,
- first integral method,
- soliton solution,
- analytic solutions
Citation: Faeza Lafta Hasan, Mohamed A. Abdoon, Rania Saadeh, Ahmad Qazza, Dalal Khalid Almutairi. Exploring analytical results for (2+1) dimensional breaking soliton equation and stochastic fractional Broer-Kaup system[J]. AIMS Mathematics, 2024, 9(5): 11622-11643. doi: 10.3934/math.2024570

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Abstract

This paper introduces a pioneering exploration of the stochastic (2+1) dimensional breaking soliton equation (SBSE) and the stochastic fractional Broer-Kaup system (SFBK), employing the first integral method to uncover explicit solutions, including trigonometric, exponential, hyperbolic, and solitary wave solutions. Despite the extensive application of the Broer-Kaup model in tsunami wave analysis and plasma physics, existing literature has largely overlooked the complexity introduced by stochastic elements and fractional dimensions. Our study fills this critical gap by extending the traditional Broer-Kaup equations through the lens of stochastic forces, thereby offering a more comprehensive framework for analyzing hydrodynamic wave models. The novelty of our approach lies in the detailed investigation of the SBSE and SFBK equations, providing new insights into the behavior of shallow water waves under the influence of randomness. This work not only advances theoretical understanding but also enhances practical analysis capabilities by illustrating the effects of noise on wave propagation. Utilizing MATLAB for visual representation, we demonstrate the efficiency and flexibility of our method in addressing these sophisticated physical processes. The analytical solutions derived here mark a significant departure from previous findings, contributing novel perspectives to the field and paving the way for future research into complex wave dynamics.

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