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

被引：79

作者：

Gao, Xin-Yi ^{[1
,2
]}

机构：

[1] North China Univ Technol, Coll Sci, Beijing 100144, Peoples R China

[2] North China Univ Technol, Beijing Key Lab Integrat & Anal Large Scale Stream, Beijing 100144, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2024年 / 23卷 / 04期

关键词：

Generalized nonlinear shallow water wave equation; B & auml; cklund transformation; Similarity reduction; Symbolic computation; Singular manifold; Soliton;

D O I：

10.1007/s12346-024-01034-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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-B & auml;cklund 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.

引用

页数：9

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