In the Shallow Water: Auto-Bäcklund, Hetero-Bäcklund and Scaling Transformations via a (2+1)-Dimensional Generalized Broer-Kaup System

These days, watching the shallow water waves, people think about the nonlinear Broer-type models, e.g., a (2+1)-dimensional generalized Broer-Kaup system modeling, e.g., certain nonlinear long waves in the shallow water. For that system, with reference to, e.g., the wave height and wave horizontal v...

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Bibliographic Details
Published in:Qualitative theory of dynamical systems 2024-09, Vol.23 (4), Article 184
Main Author: Gao, Xin-Yi
Format: Article
Language:English
Subjects:
Partial differential equations
Shallow water
Solitary waves
Water waves
Wave height
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Summary:These days, watching the shallow water waves, people think about the nonlinear Broer-type models, e.g., a (2+1)-dimensional generalized Broer-Kaup system modeling, e.g., certain nonlinear long waves in the shallow water. For that system, with reference to, e.g., the wave height and wave horizontal velocity, this paper avails of symbolic computation to obtain (A) an auto-Bäcklund transformation with some solitons; (B) a group of the scaling transformations and (C) a group of the hetero-Bäcklund transformations, to a known linear partial differential equation, from that system. Results rely on the coefficients in that system.
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-024-01025-9