The novel stochastic solutions for the Maccari system driven by Wiener perturbations

Hesham G. Abdelwahed; Mahmoud A. E. Abdelrahman; Hesham G. Abdelwahed; Mahmoud A. E. Abdelrahman

doi:10.3934/math.2026221

AIMS Mathematics

2026, Volume 11, Issue 3: 5365-5378. doi: 10.3934/math.2026221

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The novel stochastic solutions for the Maccari system driven by Wiener perturbations

Hesham G. Abdelwahed ^{1
,
,},
Mahmoud A. E. Abdelrahman ²

1.
Department of Physics, College of Science and Humanities, Al-Kharj, Prince Sattam bin Abdulaziz University, Al- Kharj11942, Saudi Arabia
2.
Department of Mathematics, College of Science, Taibah University, Madinah, Saudi Arabia

Received: 18 November 2025 Revised: 05 February 2026 Accepted: 09 February 2026 Published: 02 March 2026
MSC : 35C07, 60H15, 35Q55, 35Q70

In this paper, we look at novel stochastic solutions for the coupled Maccari system through the Wiener process. The incorporation of random perturbations provides a rigorous framework for modeling physically relevant phenomena in which noise-induced effects play a significant role. Such effects naturally arise in a wide range of applications, including signal propagation in optical fibers, plasma dynamics, and the evolution of fluid interfaces, where stochastic fluctuations can substantially influence the system behavior. To generate explicit analytical solitary wave solutions, we use the extended tanh function method (ETFM), which allows for the systematic derivation of accurate stochastic wave structures, such as soliton-like, blow up, periodic, and rational-type solutions under stochastic influence. To illustrate the propagation behavior of solitary waves in the stochastic Maccari model, 2D graphical representations of selected solutions were generated using MATLAB software. The obtained solutions demonstrate complex interactions between deterministic nonlinear dynamics and stochastic fluctuations, shedding light on the modulation and stability of wave propagation in noisy environments. These discoveries not only contribute to a better theoretical understanding of stochastic nonlinear systems, but they also have potential applications in sectors where random disturbances have a large impact on wave evolution.
- Wiener process,
- stochastic Maccari system,
- noise-driven dynamics,
- random perturbations,
- stochastic wave solutions
Citation: Hesham G. Abdelwahed, Mahmoud A. E. Abdelrahman. The novel stochastic solutions for the Maccari system driven by Wiener perturbations[J]. AIMS Mathematics, 2026, 11(3): 5365-5378. doi: 10.3934/math.2026221

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Abstract

In this paper, we look at novel stochastic solutions for the coupled Maccari system through the Wiener process. The incorporation of random perturbations provides a rigorous framework for modeling physically relevant phenomena in which noise-induced effects play a significant role. Such effects naturally arise in a wide range of applications, including signal propagation in optical fibers, plasma dynamics, and the evolution of fluid interfaces, where stochastic fluctuations can substantially influence the system behavior. To generate explicit analytical solitary wave solutions, we use the extended tanh function method (ETFM), which allows for the systematic derivation of accurate stochastic wave structures, such as soliton-like, blow up, periodic, and rational-type solutions under stochastic influence. To illustrate the propagation behavior of solitary waves in the stochastic Maccari model, 2D graphical representations of selected solutions were generated using MATLAB software. The obtained solutions demonstrate complex interactions between deterministic nonlinear dynamics and stochastic fluctuations, shedding light on the modulation and stability of wave propagation in noisy environments. These discoveries not only contribute to a better theoretical understanding of stochastic nonlinear systems, but they also have potential applications in sectors where random disturbances have a large impact on wave evolution.

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