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Dynamical analysis of Jacobian elliptic function soliton solutions, and chaotic behavior with defective tools of the stochastic PNLSE equation with multiplicative white noise

Author

Listed:
  • Roshid, Md. Mamunur
  • Abdalla, Mohamed
  • Osman, M.S.

Abstract

This manuscript presents an exclusive study on the stochastic perturbed nonlinear Schrödinger equation (SPNLSE) to check the wave propagation of light in nonlinear optical fibers. Firstly, the stochastic perturbed nonlinear Schrödinger equation is converted into a planar dynamic system using a wave transformation variable and a Galilean transformation. Secondly, the chaotic nature, super-periodicity, strange attractor, fractal dimension, and return map are analyzed using a frequency and trigonometric perturbation term. Additionally, the optical soliton solutions of the proposed model are constructed using a new Jacobian elliptic function method. The solutions encompass all trigonometric and hyperbolic functions. Using suitable values for the free parameters, the bright bell shape, dark bell shape, periodic wave, and M-shape soliton solution are illustrated through three-dimensional (3D), two-dimensional (pathline) profiles and also analyse the dynamic properties of the derived solutions. The influence of the multiplicative noise intensity is also presented for diverse values of ρ. This method demonstrates how well graphical simulations work to show how these solutions behave and interact in practical settings. The result of the comparison demonstrates that the multiplicative noise has a great influence on the obtained solutions. Additionally, the numerical stability of the obtained soliton solutions is checked by the Hamiltonian method. The obtained solutions of the proposed model are very important for figuring out how stable optical solitons are, how noise causes jitter, and how signals degrade in fiber-optic communications and nonlinear photonic systems. The multiplicative noise term is very important since it scales with the signal itself, which causes phase and amplitude noise to be associated. This can affect long-haul transmission and ultrafast pulse dynamics.

Suggested Citation

  • Roshid, Md. Mamunur & Abdalla, Mohamed & Osman, M.S., 2025. "Dynamical analysis of Jacobian elliptic function soliton solutions, and chaotic behavior with defective tools of the stochastic PNLSE equation with multiplicative white noise," Chaos, Solitons & Fractals, Elsevier, vol. 201(P2).
    • Handle: RePEc:eee:chsofr:v:201:y:2025:i:p2:s0960077925013013
    DOI: 10.1016/j.chaos.2025.117288
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    References listed on IDEAS

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    1. Kang Le Wang, 2023. "Novel Approaches To Fractional Klein–Gordon–Zakharov Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 31(07), pages 1-12.
    2. Tang, Lu, 2022. "Bifurcation analysis and multiple solitons in birefringent fibers with coupled Schrödinger-Hirota equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    3. Wael W. Mohammed & Farah M. Al-Askar & M. El-Morshedy & Arzu Akbulut, 2022. "Impact of Multiplicative Noise on the Exact Solutions of the Fractional-Stochastic Boussinesq-Burger System," Journal of Mathematics, Hindawi, vol. 2022, pages 1-10, September.
    4. Chun-Fu Wei & Kang-Le Wang, 2025. "Construction Of Novel Soliton Solutions For The Fractional Chiral Nonlinear Schrã–Dinger Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(07), pages 1-14.
    5. Kang-Le Wang, 2025. "Dynamical Analysis Of The Soliton Solutions For The Nonlinear Fractional Akbota Equation," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 33(09), pages 1-17.
    6. Liu, Xue-Ke & Wang, Zhen & Du, Ruo-Chen & Wen, Xiao-Yong, 2025. "Rogue wave dynamics and energy spectra for the generalized Heisenberg spin chain equation," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
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