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Breathers and rogue waves on the double-periodic background for the reverse-space-time derivative nonlinear Schrödinger equation

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Abstract

In the present investigation, the breathers and rogue waves on the double-periodic background are successfully constructed by Darboux transformation using a plane wave seed solution. Firstly, the Darboux transformation for the reverse-space-time derivative nonlinear Schrödinger equation is constructed. Secondly, periodic solutions, breathers, double-periodic solutions, breathers on the periodic and double-periodic background are derived by n-fold Darboux transformation. Thirdly, the higher-order rogue waves on the periodic and double-periodic background are constructed by semi-degenerate Darboux transformation. In addition, the dynamic behaviors of the solutions are plotted to show some interesting new solution structures.

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Acknowledgements

The authors would like to thank Lou Senyue, Fan Engui, Yan Zhenya, Peng Weiqi and Wang Minmin for their valuable comments and suggestions. This work was supported by National Natural Science Foundation of China (No.12175069), Global Change Research Program of China (No.2015CB953904) and Science and Technology Commission of Shanghai Municipality (No.18dz2271000).

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  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

  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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The project is supported by National Natural Science Foundation of China (No.12175069), Global Change Research Program of China (No.2015CB953904) and Science and Technology Commission of Shanghai Municipality (No.18dz2271000)

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Zhou, H., Chen, Y. Breathers and rogue waves on the double-periodic background for the reverse-space-time derivative nonlinear Schrödinger equation. Nonlinear Dyn 106, 3437–3451 (2021). https://doi.org/10.1007/s11071-021-06953-8

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