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Dynamics analysis of higher-order soliton solutions for the coupled mixed derivative nonlinear Schrödinger equation

含有混合导数项耦合非线性薛定谔方程高阶孤子解的动力学分析

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Abstract

In this paper, the dynamics of the higher-order soliton solutions for the coupled mixed derivative nonlinear Schrödinger equation are investigated via generalized Darboux transformation. Given a pair of linearly independent solutions of the Lax pair, the one- to three-soliton solutions are obtained via algebraic iteration. Furthermore, two and three solitons are respectively displayed via numerical simulation. Moreover, the dynamics of solitons are illustrated with corresponding evolution plots, such as elastic collisions, inelastic collisions, and bound states. It is found that there are some novel phenomena of interactions among solitons, which may provide a theoretical basis for studying optical solitons in experiments.

摘要

本文利用广义达布变换研究了含有混合导数项耦合非线性薛定谔方程高阶孤子的动力学特性. 基于Lax对方程的一对线性无关解, 利用代数迭代过程推导出该方程组的单孤子解到三孤子解. 通过数值模拟, 研究该方程组的二孤子和三孤子, 给出相应的动力学演化图, 展现多孤子的动力学性态–孤子的弹性碰撞、非弹性碰撞和束缚态. 研究表明, 多孤子呈现出一些新颖的相互作用方式, 这将有助于实验中对光孤子的进一步研究.

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Authors and Affiliations

  1. Department of Mathematics, North University of China, Taiyuan, 030051, China

    Ni Song  (宋妮) & Yuxiang Lei  (雷宇祥)

  2. Faculty of Materials and Manufacturing, Beijing University of Technology, Beijing, 100124, China

    Dongxing Cao  (曹东兴)

Authors
  1. Ni Song  (宋妮)
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  2. Yuxiang Lei  (雷宇祥)
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  3. Dongxing Cao  (曹东兴)
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Corresponding author

Correspondence to Ni Song  (宋妮).

Additional information

This work was supported by the National Natural Science Foundation of China (Grant No. 11602232), Shanxi Natural Science Foundation (Grant No. 201901D111179), and the Fund for Shanxi (Grant 1331KIRT).

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Song, N., Lei, Y. & Cao, D. Dynamics analysis of higher-order soliton solutions for the coupled mixed derivative nonlinear Schrödinger equation. Acta Mech. Sin. 38, 521500 (2022). https://doi.org/10.1007/s10409-021-09082-x

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