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The lump, lump off and rogue wave solutions of a (\(2+1\))-dimensional breaking soliton equation

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Abstract

In this work, the (\(2+1\))-dimensional breaking soliton equation is investigated, which can be used to describe certain properties of exact solutions. We construct the lump soliton and more general lump soliton with more arbitrary parameters via using Hirota bilinear method. Furthermore, the lump off solution is presented by considering a stripe soliton solution generated completely with the lump solution. The lump part is cut by soliton part before and after a special time. Finally, according to a pair of stripe solitons, we construct the special rogue waves by cutting the lump soliton. Our results show that the occurrence of rogue wave time and location can be captured by tracking the motion path of the lump solution and confirming when and where it collides with visible solitons.

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Acknowledgements

The authors would like to thank the editor and the referees for their valuable comments and suggestions. This work is supported by the National Natural Science Foundation of China (12001377, 52071056, 52101360, 51979032), State Key Laboratory of Coastal and Offshore Engineering (LP2104), the China Postdoctoral Science Foundation (2021M701837), the Fundamental Research Funds for the Central Universities (DUT21ZD402) and the Liaoning Revitalization Talents Program (XLYC2007109).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060, People’s Republic of China

    Yiren Chen

  2. Department of Hydraulic Engineering, Tsinghua University, Beijing, 100084, China

    Zong-Bing Yu

  3. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian, 116024, China

    Zong-Bing Yu

  4. School of Naval Architecture, Dalian University of Technology, Dalian, 116024, China

    Li Zou

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  1. Yiren Chen
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Chen, Y., Yu, ZB. & Zou, L. The lump, lump off and rogue wave solutions of a (\(2+1\))-dimensional breaking soliton equation. Nonlinear Dyn 111, 591–602 (2023). https://doi.org/10.1007/s11071-022-07823-7

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