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Exact N-soliton solutions and dynamics of two types of matrix nonlinear Schrödinger equation

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Abstract

The dynamical properties of the optical solitons in two types of matrix nonlinear Schrödin-ger (NLS) equation are studied by Riemann–Hilbert method. Firstly, the inverse scattering transform of the matrix NLS equation is investigated and the corresponding Riemann–Hilbert problem is established. Then, by solving the Riemann–Hilbert problem of discrete spectrum, the N-soliton solutions of the matrix NLS equations are obtained. Finally, the single-soliton solution, two-soliton solution and three-soliton solution of the matrix NLS equations are attained. It is proved that the two-soliton solution is decomposed into two single-soliton solutions when the time approaches infinity and the multiple solitons will overlap and form a bound state advancing at the same velocity when they have the same velocity.

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The data that support the findings of this study are available on request from the corresponding author, [Xinyu Wang], upon reasonable request.

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Xinyu Wang

  2. School of Sciences, China University of Petroleum (East China), Qingdao, 266580, China

    Hongyan Zhi

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  1. Xinyu Wang
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  2. Hongyan Zhi
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Correspondence to Xinyu Wang.

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Wang, X., Zhi, H. Exact N-soliton solutions and dynamics of two types of matrix nonlinear Schrödinger equation. Nonlinear Dyn 111, 21191–21206 (2023). https://doi.org/10.1007/s11071-023-08903-y

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