Stochastic soliton dynamics in the perturbed Gerdjikov-Ivanov equation with multiplicative noise via the new Jacobi elliptic function expansion method

Nafissa T. Trouba; Huiying Xu; Reham M. A. Shohib; Mohamed E. M. Alngar; Mohammed El-Meligy; Xinzhong Zhu; Adham E. Ragab; Nafissa T. Trouba; Huiying Xu; Reham M. A. Shohib; Mohamed E. M. Alngar; Mohammed El-Meligy; Xinzhong Zhu; Adham E. Ragab

doi:10.3934/math.20251182

AIMS Mathematics

2025, Volume 10, Issue 11: 26884-26904. doi: 10.3934/math.20251182

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Research article

Stochastic soliton dynamics in the perturbed Gerdjikov-Ivanov equation with multiplicative noise via the new Jacobi elliptic function expansion method

1.
School of Computer Science and Technology, Zhejiang Normal University, Jinhua, 321004, China
2.
Zhejiang Institute of Photoelectronics, Jinhua, Zhejiang 321004, China
3.
Basic Science Department, Faculty of Economics and Business Administration, Innovation University, Sharqia, Egypt
4.
Mathematics Education Program, Faculty of Education and Arts, Sohar University, Sohar 311, Oman
5.
Applied Science Research Center, Applied Science Private University, Amman, Jordan
6.
College of Computer Science and Artificial Intelligence, Wenzhou University, Wenzhou 325035, China
7.
Department of Industrial Engineering, College of Engineering, King Saud University, Riyadh 12372, Saudi Arabia

Received: 05 July 2025 Revised: 18 September 2025 Accepted: 09 October 2025 Published: 20 November 2025
MSC : 35C07, 35Q40, 35Q55, 60H15, 81Q15

This study investigated the perturbed Gerdjikov-Ivanov equation (PGIE) affected by multiplicative noise in the Itô sense. The equation examined the influence of stochastic perturbations on its solitonic structures through an analytical and computational method. We found precise soliton solutions and examined their stability through the new Jacobi elliptic function expansion method. Subsequent to the mathematical study, graphical representations were executed. The results enhance the comprehensive understanding of nonlinear stochastic wave equations and their applications in optical fiber communications and many physical systems. Subsequently, the three-dimensional and two-dimensional model demonstrate the presence of bright and dark solitons, Jacobi-elliptic solutions, and periodic solutions for various values of $ \sigma $.
- Gerdjikov-Ivanov equation,
- solitons,
- Itô sense
Citation: Nafissa T. Trouba, Huiying Xu, Reham M. A. Shohib, Mohamed E. M. Alngar, Mohammed El-Meligy, Xinzhong Zhu, Adham E. Ragab. Stochastic soliton dynamics in the perturbed Gerdjikov-Ivanov equation with multiplicative noise via the new Jacobi elliptic function expansion method[J]. AIMS Mathematics, 2025, 10(11): 26884-26904. doi: 10.3934/math.20251182

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Abstract

This study investigated the perturbed Gerdjikov-Ivanov equation (PGIE) affected by multiplicative noise in the Itô sense. The equation examined the influence of stochastic perturbations on its solitonic structures through an analytical and computational method. We found precise soliton solutions and examined their stability through the new Jacobi elliptic function expansion method. Subsequent to the mathematical study, graphical representations were executed. The results enhance the comprehensive understanding of nonlinear stochastic wave equations and their applications in optical fiber communications and many physical systems. Subsequently, the three-dimensional and two-dimensional model demonstrate the presence of bright and dark solitons, Jacobi-elliptic solutions, and periodic solutions for various values of $ \sigma $.

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