Soliton solutions and stability analysis of the stochastic nonlinear reaction-diffusion equation with multiplicative white noise in soliton dynamics and optical physics

Nafissa T. Trouba; Huiying Xu; Mohamed E. M. Alngar; Reham M. A. Shohib; Haitham A. Mahmoud; Xinzhong Zhu; Nafissa T. Trouba; Huiying Xu; Mohamed E. M. Alngar; Reham M. A. Shohib; Haitham A. Mahmoud; Xinzhong Zhu

doi:10.3934/math.2025086

AIMS Mathematics

2025, Volume 10, Issue 1: 1859-1881. doi: 10.3934/math.2025086

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Research article

Soliton solutions and stability analysis of the stochastic nonlinear reaction-diffusion equation with multiplicative white noise in soliton dynamics and optical physics

1.
School of Computer Science and Technology, Zhejiang Normal University, Jinhua 321004, China
2.
Zhejiang Institute of Photo-electronics, Zhejiang, Jinhua 321004, China
3.
Department of Mathematics Education, Faculty of Education & Arts, Sohar University, Sohar, Oman
4.
Basic Science Department, Higher Institute of Management Sciences & Foreign Trade, Cairo, 379, Egypt
5.
Industrial Engineering Department, College of Engineering, King Saud University, Riyadh 11421, Saudi Arabia

Received: 20 November 2024 Revised: 16 January 2025 Accepted: 22 January 2025 Published: 24 January 2025
MSC : 34L30, 35A24, 35B35, 35C08, 74J35

In this article, we explored the stochastic nonlinear reaction-diffusion (RD) equation under the influence of multiplicative white noise. To obtain novel soliton solutions, we employed two powerful analytical techniques: the unified Riccati equation expansion method and the modified Kudryashov method. These methods yield a diverse set of soliton solutions, including combo-dark solitons, dark solitons, singular solitons, combo-bright-singular solitons, and periodic wave solutions. We also performed a comprehensive stability analysis of the stochastic nonlinear RD equation with multiplicative white noise. The findings provide valuable insights into the behavior of solitons in stochastic nonlinear systems, with significant implications for fields such as mathematical physics, nonlinear science, and applied mathematics. These results hold particular relevance for soliton dynamics in optical physics, where they can be applied to improve understanding of wave propagation in noisy environments, signal transmission, and the design of robust optical communication systems.
- solitons,
- stochastic,
- nonlinear reaction-diffusion,
- multiplicative white noise,
- soliton dynamics,
- optical physics,
- wave propagation
Citation: Nafissa T. Trouba, Huiying Xu, Mohamed E. M. Alngar, Reham M. A. Shohib, Haitham A. Mahmoud, Xinzhong Zhu. Soliton solutions and stability analysis of the stochastic nonlinear reaction-diffusion equation with multiplicative white noise in soliton dynamics and optical physics[J]. AIMS Mathematics, 2025, 10(1): 1859-1881. doi: 10.3934/math.2025086

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Abstract

In this article, we explored the stochastic nonlinear reaction-diffusion (RD) equation under the influence of multiplicative white noise. To obtain novel soliton solutions, we employed two powerful analytical techniques: the unified Riccati equation expansion method and the modified Kudryashov method. These methods yield a diverse set of soliton solutions, including combo-dark solitons, dark solitons, singular solitons, combo-bright-singular solitons, and periodic wave solutions. We also performed a comprehensive stability analysis of the stochastic nonlinear RD equation with multiplicative white noise. The findings provide valuable insights into the behavior of solitons in stochastic nonlinear systems, with significant implications for fields such as mathematical physics, nonlinear science, and applied mathematics. These results hold particular relevance for soliton dynamics in optical physics, where they can be applied to improve understanding of wave propagation in noisy environments, signal transmission, and the design of robust optical communication systems.

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