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

Cailiang Chen, Mengke Yu and Qiuyan Zhang ()
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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

Mathematics, 2025, vol. 13, issue 12, 1-25

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.

Keywords: Kudryashov’s quintic power law; refractive index; nonlinear Schrödinger equation; bifurcation; periodic solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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