https://doi.org/10.1140/epjp/s13360-024-05082-6
Regular Article
Dynamics of heterotypic soliton, high-order breather, M-lump wave, and multi-wave interaction solutions for a (
)-dimensional Kadomtsev–Petviashvili equation
1
The Engineering and Technical College of Chengdu University of Technology, 614000, Leshan, China
2
Visual Computing and Virtual Reality Key Laboratory of Sichuan Province, Sichuan Normal University, 610068, Chengdu, China
3
Southwestern Institute of Physics, 610225, Chengdu, China
Received:
3
November
2023
Accepted:
11
March
2024
Published online:
25
March
2024
In this study, we investigate a (3+1)-dimensional KP equation, which is widely used to model the behavior of nonlinear waves in plasma physics and fluid mechanics. First, the multi-soliton solutions of the equation are derived using the Hirota bilinear method. Based on the multi-soliton solutions, heterotypic soliton is obtained by setting the partial dispersion coefficient to zero. Under the complex conjugation of the parameters, high-order breather waves are derived. Additionally, the M-lump wave solutions of the equation are derived by applying the long-wave limit. To gain a deeper understanding of its physical dynamics, we conducted numerical simulations to simulate various characteristics of M-lump waves during their propagation, including their peaks, troughs, propagation velocities, and propagation trajectories. Afterward, by combining the long-wave limit with the complex conjugation of the parameters, we discuss three types of multi-wave interaction phenomena described by this equation and illustrate the collision process between waves in graphical form.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. 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.
