https://doi.org/10.1140/epjp/s13360-022-03574-x
Regular Article
Pfaffian, soliton, hybrid and periodic-wave solutions for a (
)-dimensional B-type Kadomtsev–Petviashvili equation in fluid mechanics
Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, 100191, Beijing, China
b
gaoyt163@163.com
c
yuxin@buaa.edu.cn
Received:
1
August
2022
Accepted:
30
November
2022
Published online:
3
January
2023
Propagation of the long waves can be described via certain high-dimensional and high-order equations in fluid mechanics. This paper is focused on a ()-dimensional B-type Kadomtsev–Petviashvili (BKP) equation in fluid mechanics. We verify the Nth-order Pfaffian solutions for the BKP equation via the Pfaffian technique, where N is a positive integer. We construct the N-soliton solutions for the BKP equation via the Nth-order Pfaffian solutions. Elastic interaction and inelastic interaction as well as soliton resonance between the two solitons are analyzed, and influence of the coefficients in the BKP equation on the interaction between the two solitons is studied via the asymptotic analysis. For the BKP equation, three solitons and hybrid solutions composed of the one breather and one soliton are illustrated graphically. We give the one-periodic-wave solutions for the BKP equation via the Hirota-Riemann method. We study the relation between the one-periodic-wave solutions and one-soliton solutions. We find that the one-periodic-wave solutions can approach to the one-soliton solutions under certain conditions.
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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.
