卡马萨-霍尔姆型两个 2 分量方程的非局部对称性

IF 1 4区 物理与天体物理 Q3 PHYSICS, MATHEMATICAL
Ziqi Li, Kai Tian
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引用次数: 0

摘要

对于一个(2)分量的卡马萨-霍尔姆方程,以及一个(2)分量的修正卡马萨-霍尔姆方程的广义化,非局部无穷小对称性与线性谱问题的特征函数二次相关,是由谱参数的函数梯度构造的。利用适当的伪势,这些非局部无穷小对称性被扩展到放大系统,然后显式积分,为放大系统生成有限形式的对称性变换。作为这些有限对称变换的实现,推导出了这两个方程的某些非难解和贝克隆变换。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Nonlocal symmetries of two 2-component equations of Camassa–Holm type

For a \(2\)-component Camassa–Holm equation, as well as a \(2\)-component generalization of the modified Camassa–Holm equation, nonlocal infinitesimal symmetries quadratically dependent on eigenfunctions of linear spectral problems are constructed from functional gradients of spectral parameters. With appropriate pseudopotentials, these nonlocal infinitesimal symmetries are prolonged to enlarged systems, and then explicitly integrated to generate symmetry transformations in finite form for the enlarged systems. As implementations of these finite symmetry transformations, some kinds of nontrivial solutions and Bäcklund transformations are derived for both equations.

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来源期刊
Theoretical and Mathematical Physics
Theoretical and Mathematical Physics 物理-物理:数学物理
CiteScore
1.60
自引率
20.00%
发文量
103
审稿时长
4-8 weeks
期刊介绍: Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems. Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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