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Periodic-wave and semirational solutions for the (2 \(+\) 1)-dimensional Davey–Stewartson equations on the surface water waves of finite depth

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Abstract

The (2 \(+\) 1)-dimensional Davey–Stewartson equations concerning the evolution of surface water waves with finite depth are studied. We derive the periodic-wave solutions through the Kadomtsev–Petviashvili hierarchy reduction. We obtain the growing-decaying periodic wave and three kinds of breathers via those solutions. We obtain the periodic wave takes on the growing and decaying property. Taking the long-wave limit on the periodic-wave solutions, we derive the semirational solutions describing the interaction of the rogue wave, lump, breather and periodic wave. We illustrate the lump and rogue wave and find that the rogue wave (lump) is the long-wave limit of the periodic wave (breather).

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Acknowledgements

This work has been supported by the National Natural Science Foundation of China under Grant Nos. 11772017 and 11805020, by the Open Fund of State Key Laboratory of Information Photonics and Optical Communications (Beijing University of Posts and Telecommunications), China (IPOC:2017ZZ05), and by the Beijing University of Posts and Telecommunications Excellent Ph.D. Students Foundation (No. CX2019321).

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Authors and Affiliations

  1. State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Yu-Qiang Yuan, Bo Tian, Xue-Hui Zhao & Xia-Xia Du

  2. School of Information, University of International Business and Economics, Beijing, 100029, China

    Qi-Xing Qu

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  1. Yu-Qiang Yuan
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Yuan, YQ., Tian, B., Qu, QX. et al. Periodic-wave and semirational solutions for the (2 \(+\) 1)-dimensional Davey–Stewartson equations on the surface water waves of finite depth. Z. Angew. Math. Phys. 71, 46 (2020). https://doi.org/10.1007/s00033-020-1252-6

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  • DOI: https://doi.org/10.1007/s00033-020-1252-6

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