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Complex excitations for the derivative nonlinear Schrödinger equation

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Abstract

The Darboux transformation (DT) formulae for the derivative nonlinear Schrödinger (DNLS) equation are expressed in concise forms, from which the multi-solitons, n-periodic solutions, higher-order hybrid-pattern solitons and some mixed solutions are obtained. These complex excitations can be constructed thanks to more general semi-degenerate DTs. Even the nondegenerate N-fold DT with a zero seed can generate complicated n-periodic solutions. It is proved that the solution q[N] at the origin depends only on the summation of the spectral parameters. We find the maximum amplitudes of several classes of the wave solutions are determined by the summation. Many interesting phenomena are discovered from these new solutions. For instance, the interactions between n-periodic waves produce peaks with different amplitudes and sizes. A soliton on a single-periodic wave background shares a similar feature as a breather due to the interference of the periodic background. In addition, the results are extended to the reverse-space-time DNLS equation.

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Funding

This work was supported by National Natural Science Foundation of China (No.12175069), Global Change Research Program of China (No.2015CB953904), Science and Technology Commission of Shanghai Municipality (No.18dz2271000 and No.21JC1402500).

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Authors and Affiliations

  1. School of Mathematical Sciences, Shanghai Key, Laboratory of PMMP, East China Normal University, Shanghai, 200241, People’s Republic of China

    Huijuan Zhou, Yong Chen, Xiaoyan Tang & Yuqi Li

  2. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, People’s Republic of China

    Yong Chen

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  1. Huijuan Zhou
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  2. Yong Chen
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  3. Xiaoyan Tang
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  4. Yuqi Li
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Correspondence to Yong Chen.

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Zhou, H., Chen, Y., Tang, X. et al. Complex excitations for the derivative nonlinear Schrödinger equation. Nonlinear Dyn 109, 1947–1967 (2022). https://doi.org/10.1007/s11071-022-07521-4

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