From optical solitons to chaos: stochastic dynamics in nonlinear Schrödinger systems

Saad Althobaiti; Hamood Ur Rehman; Saad Althobaiti; Hamood Ur Rehman

doi:10.3934/math.2026599

AIMS Mathematics

2026, Volume 11, Issue 5: 14617-14640. doi: 10.3934/math.2026599

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Research article

From optical solitons to chaos: stochastic dynamics in nonlinear Schrödinger systems

Saad Althobaiti ¹,
Hamood Ur Rehman ^{2
,
,}

1.
Department of Science and Technology, University College Ranyah, Taif University, Ranyah 21975, Saudi Arabia
2.
Department of Mathematics, University of Okara, Okara, Pakistan

Received: 20 January 2026 Revised: 29 April 2026 Accepted: 11 May 2026 Published: 25 May 2026
MSC : 35Q51, 35Q55

This paper considers the stochastic nonlinear Schrödinger equation with Brownian motion for the representation of noise effects in the propagation of waves. Using the modified Sardar sub-equation method, exact solutions of the solitons and periodic type are constructed. The effect of stochastic perturbation on the solutions is studied revealing the formation of deformations and instabilities. The chaotic nature of the system is further verified under the effects of sinusoidal, cosine, hyperbolic, and Gaussian perturbations through numerical experiments. Phase diagrams and time series show a very complex non-periodic pattern. Sensitivity to the initial condition proves that the solution is highly sensitive to changes in the initial values.
- optical solitons,
- phase portraits,
- Brownian motion,
- modified Sardar subequation method
Citation: Saad Althobaiti, Hamood Ur Rehman. From optical solitons to chaos: stochastic dynamics in nonlinear Schrödinger systems[J]. AIMS Mathematics, 2026, 11(5): 14617-14640. doi: 10.3934/math.2026599

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Abstract

This paper considers the stochastic nonlinear Schrödinger equation with Brownian motion for the representation of noise effects in the propagation of waves. Using the modified Sardar sub-equation method, exact solutions of the solitons and periodic type are constructed. The effect of stochastic perturbation on the solutions is studied revealing the formation of deformations and instabilities. The chaotic nature of the system is further verified under the effects of sinusoidal, cosine, hyperbolic, and Gaussian perturbations through numerical experiments. Phase diagrams and time series show a very complex non-periodic pattern. Sensitivity to the initial condition proves that the solution is highly sensitive to changes in the initial values.

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