Dynamical properties, chirped solutions, and chaotic behaviors of the extended nonlinear Schrödinger equation

In this paper, we focus on an extended nonlinear Schrödinger equation describing the pulse propagation in a nonlinear Schrödinger equation with self‐steepening and magneto‐optic effects. The existence of periodic and solitary solutions are proved based on the bifurcation method, and also, the Hamilt...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-06, Vol.47 (9), p.7473-7487
Main Author: Tang, Jia‐Xuan
Format: Article
Language:English
Subjects:
bifurcation method
chaotic behavior
chirped solutions
complete discrimination system for polynomial method
extended nonlinear Schrödinger equation
Polynomials
Pulse propagation
Schrodinger equation
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Summary:In this paper, we focus on an extended nonlinear Schrödinger equation describing the pulse propagation in a nonlinear Schrödinger equation with self‐steepening and magneto‐optic effects. The existence of periodic and solitary solutions are proved based on the bifurcation method, and also, the Hamiltonian properties and the classification of its equilibrium points are obtained. The chirped solutions of the extended nonlinear Schrödinger equations are obtained by using the complete discrimination system for polynomial method, and under specific parameter conditions, three types of optical wave patterns are obtained to visualize the model. In particular, we consider the external perturbation terms to analyze the chaotic behavior of this equation.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9983