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The nonlinear superposition between anomalous scattering of lumps and other waves for KPI equation

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Abstract

Normally, lump waves with different velocities and amplitudes produce different phase shifts when they collide with line or breather waves. Based on the Gram determinant form of the solution, we consider a new hybrid solution consisting of two weakly interacting lump waves and line waves by means of some clever limit tricks for the Kadomtsev–Petviashvili I equation. In this new hybrid solution, each lump wave moves along the curve with a variable velocity, and lump waves have the same velocity and amplitude as |t| tends to infinity. Moreover, it is interesting that anomalous scattered lump waves exhibit the same dynamical properties when they collide with the line wave. The same phenomena also exist in the nonlinear superposition between anomalous scattering of lumps and breather waves.

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Acknowledgements

This research is supported by the Natural Science Foundation of Guangdong Province of China (No. 2021A1515012214), the Science and Technology Program of Guangzhou (No. 2019050001), National Natural Science Foundation of China (No. 12175111), and K.C.Wong Magna Fund in Ningbo University. The authors sincerely thank Dr. Xiangyu Yang (Dalian University of Technology) for the discussions and Dr. Ling An (South China University of Technology) for her help.

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Authors and Affiliations

  1. Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou, 510631, People’s Republic of China

    Zhao Zhang & Qi Guo

  2. School of Mathematics and Statistics, Ningbo University, Ningbo, 315211, People’s Republic of China

    Biao Li

  3. Department of Mathematics and Institute of Nonlinear Analysis, Lishui University, Lishui, 323000, People’s Republic of China

    Junchao Chen

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  1. Zhao Zhang
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  2. Biao Li
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  3. Junchao Chen
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  4. Qi Guo
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Correspondence to Qi Guo.

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Zhang, Z., Li, B., Chen, J. et al. The nonlinear superposition between anomalous scattering of lumps and other waves for KPI equation. Nonlinear Dyn 108, 4157–4169 (2022). https://doi.org/10.1007/s11071-022-07457-9

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