Peculiarities of resonant interactions of lump chains within the KP1 equation
Article
Article Title | Peculiarities of resonant interactions of lump chains within the KP1 equation |
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ERA Journal ID | 1014 |
Article Category | Article |
Authors | Zhang, Zhao (Author), Li, Biao (Author), Chen, Junchao (Author), Guo, Qi (Author) and Stepanyants, Yury (Author) |
Journal Title | Physica Scripta: an international journal for experimental and theoretical physics |
Journal Citation | 97 (11), pp. 1-14 |
Article Number | 115205 |
Number of Pages | 14 |
Year | 2022 |
Publisher | IOP Publishing |
Place of Publication | United Kingdom |
ISSN | 0031-8949 |
0281-1847 | |
1402-4896 | |
Digital Object Identifier (DOI) | https://doi.org/10.1088/1402-4896/ac99aa |
Web Address (URL) | https://iopscience.iop.org/article/10.1088/1402-4896/ac99aa |
Abstract | Using the Hirota bilinear method, we derive resonant solutions to the KP1 equation. Solutions describe lump chains differently oriented in (x, y)-plane. We show that resonant solutions arise as the limiting case of more general non-resonant solutions when phase shifts of lump chains caused by their interaction become infinite. Resonant solutions can describe both stationary patterns (for example, Y-shaped patterns consisting of three different lump chains) and non-stationary interacting parallel lump chains. In the latter case, a lump chain can be emitted/absorbed by another lump chain. As the number of lump chains increases, resonance phenomena become more complex and diversified including the cases of exchange of a lump chain by two other lump chains. The method used in this paper can be extended to apply to other integrable systems in two and three spatial dimensions such as, for example, described by Mel'nikov's equations. |
Keywords | Kadomtsev–Petviashvili equation, soliton, lump, resonant interaction |
ANZSRC Field of Research 2020 | 490109. Theoretical and applied mechanics |
510399. Classical physics not elsewhere classified | |
Public Notes | Files associated with this item cannot be displayed due to copyright restrictions. |
Byline Affiliations | South China Normal University, China |
NingboTech University, China | |
Lishui University, China | |
School of Mathematics, Physics and Computing | |
Institution of Origin | University of Southern Queensland |
https://research.usq.edu.au/item/q7vwz/peculiarities-of-resonant-interactions-of-lump-chains-within-the-kp1-equation
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