Dynamics of solitary waves in the stochastic complex coupled Kuralay model

Sadia Yasin; Beenish; Salma Trabelsi; Meraa Arab; Sadia Yasin; Beenish; Salma Trabelsi; Meraa Arab

doi:10.3934/math.2026251

AIMS Mathematics

2026, Volume 11, Issue 3: 6050-6079. doi: 10.3934/math.2026251

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Research article

Dynamics of solitary waves in the stochastic complex coupled Kuralay model

1.
Department of Mathematics, University of Okara 56130, Punjab, Pakistan
2.
Department of Mathematics, Quaid-Ⅰ-Azam University 45320, Islamabad, Pakistan
3.
Department of Mathematics and Statistics, College of Science, King Faisal University, Al Ahsa 31982, Saudi Arabia

Received: 16 October 2025 Revised: 25 February 2026 Accepted: 04 March 2026 Published: 10 March 2026
MSC : 26A48, 26A51, 33B10, 37K40, 39B62

In this article, we study the stochastic complex coupled Kuralay model, which possesses some applications in various fields, including physics, biology, and engineering, to obtain new solitary wave solutions. The explicit analytical solutions are obtained by using the Sardar subequation method, which helps to illuminate the dynamics of oscillators under random (noisy) effects. The integration of the Wiener process along a given method is a precise approximation of the stochastic behavior of the system. The proposed strategy enables the derivation of several exact solitary wave solutions under stochastic conditions, including bright, dark, and singular wave profiles. More significantly, the obtained solutions are also represented by 3D surface and contour plots that clearly show how solitary waves change and evolve when noise is introduced. Other stochastic models in physics and engineering can use the proposed approach to understand the workings of complex systems.
- Sardar sub-equation method,
- stochastic complex coupled Kuralay model,
- solitary wave solutions,
- Wiener process,
- multiplicative noise,
- exact solutions
Citation: Sadia Yasin, Beenish, Salma Trabelsi, Meraa Arab. Dynamics of solitary waves in the stochastic complex coupled Kuralay model[J]. AIMS Mathematics, 2026, 11(3): 6050-6079. doi: 10.3934/math.2026251

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Abstract

In this article, we study the stochastic complex coupled Kuralay model, which possesses some applications in various fields, including physics, biology, and engineering, to obtain new solitary wave solutions. The explicit analytical solutions are obtained by using the Sardar subequation method, which helps to illuminate the dynamics of oscillators under random (noisy) effects. The integration of the Wiener process along a given method is a precise approximation of the stochastic behavior of the system. The proposed strategy enables the derivation of several exact solitary wave solutions under stochastic conditions, including bright, dark, and singular wave profiles. More significantly, the obtained solutions are also represented by 3D surface and contour plots that clearly show how solitary waves change and evolve when noise is introduced. Other stochastic models in physics and engineering can use the proposed approach to understand the workings of complex systems.

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