针对广义非线性浅水波方程的孤子和相似性还原自动贝克隆变换

IF 1.9 3区数学 Q1 MATHEMATICS

Qualitative Theory of Dynamical Systems Pub Date : 2024-05-04 DOI:10.1007/s12346-024-01034-8

Xin-Yi Gao

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引用次数: 0

摘要

对浅水波的研究属于科学和工程领域的前沿问题。本文引入符号计算，针对与水的位移和速度有关的广义非线性浅水波方程，我们建立了一个自动贝克隆变换，其中包含一些孤子解，以及一组相似性还原，后者应侧重于已知的常微分方程。我们的结果与引力和波高有关。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

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

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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来源期刊

Qualitative Theory of Dynamical Systems MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.50

自引率

14.30%

发文量

130

期刊介绍： Qualitative Theory of Dynamical Systems (QTDS) publishes high-quality peer-reviewed research articles on the theory and applications of discrete and continuous dynamical systems. The journal addresses mathematicians as well as engineers, physicists, and other scientists who use dynamical systems as valuable research tools. The journal is not interested in numerical results, except if these illustrate theoretical results previously proved.