https://doi.org/10.1140/epjp/s13360-024-05536-x
Regular Article
Soliton solutions of the 
-dimensional Kaup system for water waves
School of Science, Dalian Maritime University, 116026, Dalian, China
Received:
26
October
2023
Accepted:
4
August
2024
Published online:
17
August
2024
Soliton solutions in Gram determinant of the -dimensional Kaup system have been studied based on the Kadomtsev-Petviashvili hierarchy reduction method. Such system has been used to describe the water waves propagating in an infinite narrow channel of constant mean depth. Propagation of one soliton and interactions between two solitons have been discussed. u and v components are shock profiles, while the R component presents the bell-shaped or the depression profiles. There are three types of the elastic interactions between two solitons of R component: bell-bell, bell-depression and depression-depression. Soliton fission and fusion have also been addressed, and two solitons shares the Y-type resonance. N-soliton solutions in Wronskian determinant and the corresponding Maya diagrams have also been presented. Finally, a conditionally stable finite difference scheme is proposed to numerically study solitons and verify that the soliton solution is stable.
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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.
