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

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...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2020-04, Vol.71 (2), Article 46
Main Authors: Yuan, Yu-Qiang, Tian, Bo, Qu, Qi-Xing, Zhao, Xue-Hui, Du, Xia-Xia
Format: Article
Language:English
Subjects:
Breathers
Engineering
Mathematical analysis
Mathematical Methods in Physics
Surface water
Theoretical and Applied Mechanics
Water waves
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Summary: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).
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-020-1252-6