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Wave structures and the chaotic behaviors of the cubic-quartic nonlinear Schrödinger equation for parabolic law in birefringent fibers

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Abstract

In this paper, we study the cubic-quartic nonlinear Schrödinger equation for the parabolic law through birefringent fibers by the complete discrimination system for polynomial method and obtain the solutions, dynamic system and chaotic behaviors of cubic-quartic nonlinear Schrödinger equation. Firstly, we verify the existence of solitons and periodic solutions by complete discrimination system for polynomial method. In order to confirm our findings, we show the corresponding solutions and construct some new solutions, which makes our conclusion more complete. In particular, we consider the perturbed form of the cubic-quartic complete discrimination system for polynomial method and show the chaotic behaviors of the equation via the largest Lyapunov exponents and the corresponding phase diagrams. As far as we know, the chaotic behaviors of cubic-quartic nonlinear Schrödinger equation are firstly presented.

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  1. Center of Intelligent Computing and Applied Statistics School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620, China

    Yaxi Li & Yue Kai

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  1. Yaxi Li
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  2. Yue Kai
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Correspondence to Yue Kai.

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Li, Y., Kai, Y. Wave structures and the chaotic behaviors of the cubic-quartic nonlinear Schrödinger equation for parabolic law in birefringent fibers. Nonlinear Dyn 111, 8701–8712 (2023). https://doi.org/10.1007/s11071-023-08291-3

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