New solitary waveforms and their dynamics in the stochastic generalized Chen–Lee–Liu model

Ahmed M. Elsherbeny; Taher A. Nofal; Yakup Yıldırım; Ahmed H. Arnous; Ahmed M. Elsherbeny; Taher A. Nofal; Yakup Yıldırım; Ahmed H. Arnous

doi:10.3934/math.2025239

AIMS Mathematics

2025, Volume 10, Issue 3: 5197-5235. doi: 10.3934/math.2025239

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New solitary waveforms and their dynamics in the stochastic generalized Chen–Lee–Liu model

1.
Department of Physics and Mathematics Engineering, Faculty of Engineering, Ain Shams University, Cairo 11517, Egypt
2.
Department of Mathematics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia
3.
Department of Computer Engineering, Biruni University, Istanbul 34010, Turkey
4.
Mathematics Research Center, Near East University, Nicosia 99138, Cyprus
5.
Department of Physics and Engineering Mathematics, Higher Institute of Engineering, El–Shorouk Academy, Cairo, Egypt

Received: 14 December 2024 Revised: 19 February 2025 Accepted: 25 February 2025 Published: 10 March 2025
MSC : 35Q55, 35Q60, 35Q61

This paper explores the dynamics of the generalized Chen-Lee-Liu equation, a fundamental model in nonlinear optics, extended to incorporate multiplicative white noise. By employing Itô calculus, the stochastic behavior of the system was is rigorously analyzed, providing insights into the effects of perturbations on soliton dynamics. The improved extended modified tanh-function approach was utilized to derive a variety of soliton solutions, including singular, dark, and bright solitons, as well as newly identified straddled solitons. This analytical approach highlights the transformative relationships between soliton types under specific conditions, expanding the spectrum of known solutions. The incorporation of multiplicative white noise reveals intricate changes in soliton stability, amplitude, and velocity, illustrating the interplay between deterministic and stochastic influences. These findings offer theoretical advancements in the understanding of soliton behavior in noisy environments and have practical implications for optical communication systems and nonlinear wave modeling. This study enriches the theoretical landscape of soliton dynamics and sets the stage for future research into stochastic soliton systems.
- Wiener process,
- solitons,
- perturbations,
- Chen-Lee-Liu equation,
- multiplicative white noise
Citation: Ahmed M. Elsherbeny, Taher A. Nofal, Yakup Yıldırım, Ahmed H. Arnous. New solitary waveforms and their dynamics in the stochastic generalized Chen–Lee–Liu model[J]. AIMS Mathematics, 2025, 10(3): 5197-5235. doi: 10.3934/math.2025239

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Abstract

This paper explores the dynamics of the generalized Chen-Lee-Liu equation, a fundamental model in nonlinear optics, extended to incorporate multiplicative white noise. By employing Itô calculus, the stochastic behavior of the system was is rigorously analyzed, providing insights into the effects of perturbations on soliton dynamics. The improved extended modified tanh-function approach was utilized to derive a variety of soliton solutions, including singular, dark, and bright solitons, as well as newly identified straddled solitons. This analytical approach highlights the transformative relationships between soliton types under specific conditions, expanding the spectrum of known solutions. The incorporation of multiplicative white noise reveals intricate changes in soliton stability, amplitude, and velocity, illustrating the interplay between deterministic and stochastic influences. These findings offer theoretical advancements in the understanding of soliton behavior in noisy environments and have practical implications for optical communication systems and nonlinear wave modeling. This study enriches the theoretical landscape of soliton dynamics and sets the stage for future research into stochastic soliton systems.

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