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Degenerate lump wave solutions of the Mel’nikov equation

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Abstract

The anomalous scattering of lump waves within the framework of the Mel’nikov equation is considered via Hirota’s bilinear method and further limits. The anomalous scattering phenomena of two lumps are studied in detail, asymptotic behavior of anomalous scattering lumps is discussed. Furthermore, several interesting patterns of high-order degenerate lumps are observed, including triangular and quadrangular peak locations. These exotic structures may enrich our understanding of the nature of lump waves.

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Acknowledgements

Project was supported by National Natural Science Foundation of China (Grant Nos. 52171251, U2106225), LiaoNing Revitalization Talents Program (XLYC1907014) and the Fundamental Research Funds for the Central Universities (DUT21ZD205).

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Authors and Affiliations

  1. School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China

    Xiangyu Yang & Zhen Wang

  2. Guangdong Provincial Key Laboratory of Nanophotonic Functional Materials and Devices, South China Normal University, Guangzhou, 510631, China

    Zhao Zhang

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  1. Xiangyu Yang
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Correspondence to Zhen Wang.

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Yang, X., Zhang, Z. & Wang, Z. Degenerate lump wave solutions of the Mel’nikov equation. Nonlinear Dyn 111, 1553–1563 (2023). https://doi.org/10.1007/s11071-022-07874-w

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