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Novel soliton solutions of the (3+1)-dimensional stochastic nonlinear Schrödinger equation in birefringent fibers

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  • Zayed, Elsayed M.E.
  • Ahmed, Manar S.
  • Arnous, Ahmed H.
  • Yıldırım, Yakup

Abstract

The paper studies novel solitary waves with the (3+1)-dimensional nonlinear Schrödinger equation in birefringent fibers having a white noise effect. This model is reported in this paper for the first time, guaranteeing that the analysis and results are novel and original. To investigate this model, we implement two techniques, namely, the projective Riccati equation method and the enhanced direct algebraic method. The obtained solutions are bright solitons, dark solitons, singular solitons, and straddled solitons. Besides these solitons, Jacobi and Weierstrass elliptic solutions are also obtained. These findings expand our understanding of nonlinear wave propagation in birefringent fibers under the influence of white noise and introduce new mathematical methods for solving complex nonlinear differential equations. The study opens up new directions for future research in nonlinear optical phenomena, encouraging the exploration of other nonlinear models in optical fibers and beyond.

Suggested Citation

  • Zayed, Elsayed M.E. & Ahmed, Manar S. & Arnous, Ahmed H. & Yıldırım, Yakup, 2025. "Novel soliton solutions of the (3+1)-dimensional stochastic nonlinear Schrödinger equation in birefringent fibers," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    • Handle: RePEc:eee:chsofr:v:194:y:2025:i:c:s0960077925001651
    DOI: 10.1016/j.chaos.2025.116152
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    References listed on IDEAS

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    1. Vikas Kumar & Ram Jiwari & Aloev Rakhmatullo Djurayevich & Mirzoali Urazaliyevich Khudoyberganov & Elena Guardo, 2022. "Hyperbolic (3+1)-Dimensional Nonlinear Schrödinger Equation: Lie Symmetry Analysis and Modulation Instability," Journal of Mathematics, Hindawi, vol. 2022, pages 1-8, August.
    2. Anjan Biswas & Jose Vega-Guzman & Yakup Yıldırım & Luminita Moraru & Catalina Iticescu & Abdulah A. Alghamdi, 2023. "Optical Solitons for the Concatenation Model with Differential Group Delay: Undetermined Coefficients," Mathematics, MDPI, vol. 11(9), pages 1-14, April.
    3. Wen-Xiu Ma, 2024. "Soliton Solutions to Sasa–Satsuma-Type Modified Korteweg–De Vries Equations by Binary Darboux Transformations," Mathematics, MDPI, vol. 12(23), pages 1-15, November.
    4. Yakup Yıldırım & Anjan Biswas & Luminita Moraru & Abdulah A. Alghamdi, 2023. "Quiescent Optical Solitons for the Concatenation Model with Nonlinear Chromatic Dispersion," Mathematics, MDPI, vol. 11(7), pages 1-25, April.
    5. Li Cheng & Wen-Xiu Ma, 2023. "Similarity Transformations and Nonlocal Reduced Integrable Nonlinear Schrödinger Type Equations," Mathematics, MDPI, vol. 11(19), pages 1-8, September.
    6. Ma, Wen-Xiu & Lee, Jyh-Hao, 2009. "A transformed rational function method and exact solutions to the 3+1 dimensional Jimbo–Miwa equation," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1356-1363.
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    1. Arnous, Ahmed H., 2025. "Lie symmetries, stability, and chaotic dynamics of solitons in nematic liquid crystals with stochastic perturbation," Chaos, Solitons & Fractals, Elsevier, vol. 199(P2).

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