https://doi.org/10.1140/epjp/s13360-025-06322-z
Regular Article
Elastic and inelastic collisions in the (2 + 1)-dimensional modified dispersive water wave equation
1
College of Science, University of Shanghai for Science and Technology, 200093, Shanghai, China
2
College of Science, Kaili University, 556011, Kaili, Guizhou, China
a 656361362@qq.com, qhdfqj@126.com
Received:
4
October
2024
Accepted:
12
April
2025
Published online:
13
May
2025
The research objective of this paper is to improve the exp [-ϕ(ξ)] expansion method and discuss elastic and inelastic collisions (the fusion and fission) of multiple localized waves. Based on variable separation transformation, a series of new variable separation solutions for the (2 + 1)-dimensional modified dispersive water wave equation are constructed using the improved exp[-ϕ(ξ)]] expansion method. By introducing some appropriate functions, the three-dimensional images of variable separation solutions are provided to investigate the structural characteristics and dynamic behavior of these solutions. The variable separation solutions exhibit two inelastic collisions phenomena: multiple dromion waves fuse into one dromion wave, and one periodic dromion wave splits into multiple periodic dromion waves. In addition, the “head-on” elastic collision, “chasing” elastic collision, and “head on-chasing” elastic collision of multiple periodic dromion waves are discussed, as well as the inelastic collision of two dromion solitons in a plane (on a periodic background). It is hoped that the interaction phenomenon of nonlinear waves discussed in this paper can provide a certain positive effect on the study of soliton theory.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
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.
