Auto-Bäcklund Transformation with the Solitons and Similarity Reductions for a Generalized Nonlinear Shallow Water Wave Equation

Xin-Yi Gao

Ayuda

Auto-Bäcklund Transformation with the Solitons and Similarity Reductions for a Generalized Nonlinear Shallow Water Wave Equation

Autores: Xin-Yi Gao
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 23, Nº 4, 2024
Idioma: inglés
DOI: 10.1007/s12346-024-01034-8
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Resumen
- Studies on the shallow water waves belong to the cutting-edge issues in sciences and engineering. In this paper, introducing symbolic computation, for a generalized nonlinear shallow water wave equation, with respect to the displacement and velocity of the water, we establish an auto-Bäcklund transformation with some solitonic solutions, as well as a set of the similarity reductions, the latter of which ought to be focused towards a known ordinary differential equation. Our results are seen to tie to the gravitational force and wave height.
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