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The Bifurcation and Exact Solution of the Nonlinear Schrödinger Equation with Kudryashov’s Quintic Power Law of the Refractive Index Together with the Dual Form of Nonlocal Nonlinearity

Author

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  • Cailiang Chen

    (College of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, China)

  • Mengke Yu

    (College of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, China)

  • Qiuyan Zhang

    (College of Applied Mathmatics, Chengdu University of Information Technology, Chengdu 610225, China)

Abstract

This study investigates a nonlinear Schrödinger equation that includes Kudryashov’s quintic power-law refractive index along with dual-form nonlocal nonlinearity. Employing dynamical systems theory, we analyze the model through a traveling-wave transformation, reducing it to a singular yet integrable traveling-wave system. The dynamical behavior of the corresponding regular system is examined, revealing phase trajectories bifurcations under varying parameter conditions. Furthermore, explicit solutions—including periodic, homoclinic, and heteroclinic solutions—are derived for distinct parameter regimes.

Suggested Citation

  • Cailiang Chen & Mengke Yu & Qiuyan Zhang, 2025. "The Bifurcation and Exact Solution of the Nonlinear Schrödinger Equation with Kudryashov’s Quintic Power Law of the Refractive Index Together with the Dual Form of Nonlocal Nonlinearity," Mathematics, MDPI, vol. 13(12), pages 1-25, June.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:12:p:1922-:d:1675042
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    References listed on IDEAS

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    1. Mengke Yu & Cailiang Chen & Qiuyan Zhang, 2023. "Bifurcations and Exact Solutions of the Generalized Radhakrishnan–Kundu–Lakshmanan Equation with the Polynomial Law," Mathematics, MDPI, vol. 11(20), pages 1-28, October.
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