https://doi.org/10.1140/epjp/s13360-023-03886-6
Regular Article
Extended (2+1)-dimensional Kadomtsev-Petviashvili equation in fluid mechanics: solitons, breathers, lumps and interactions
State Key Laboratory of Information Photonics and Optical Communications, and School of Science, Beijing University of Posts and Telecommunications, 100876, Beijing, China
a
yuanshen@bupt.edu.cn
b
tian_bupt@163.com
Received:
16
September
2022
Accepted:
10
March
2023
Published online:
1
April
2023
Investigations into the nonlinear phenomena in fluid mechanics are of interest. In this paper, we study an extended (2+1)-dimensional Kadomtsev-Petviashvili equation in fluid mechanics. A bilinear form of that equation is obtained via the Hirota method. With the aid of that bilinear form, N-soliton solutions are constructed, based on which the Mth-order breather and Hth-order lump solutions are determined through the complex conjugated transformations and long-wave limit method, respectively, where N, M and H are the integers. Furthermore, we derive the hybrid solutions composed of the first-order breather and one soliton, first-order lump and one soliton, and first-order lump and first-order breather. Via the aforementioned solutions, we present the (1) elastic interactions between the two solitons/breathers/lumps, (2) elastic interaction among the three solitons, (3) one lump/breather, (4) elastic interaction between the one breather and one soliton, (5) elastic interaction between the one lump and one soliton, and (6) elastic interaction between the one lump and one breather.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.