非线性波方程的渐近可整性

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2024-11-01 DOI:10.1063/5.0227082
A M Kamchatnov
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引用次数: 0

摘要

我们在非线性波方程理论中引入了渐近可积分性的概念。这意味着描述高频波包传播的方程的哈密顿结构在大尺度背景波的流体动力演化过程中得以保留,从而使这些方程具有额外的运动积分。这一条件在数学上可以表示为载波数与背景变量函数的方程组。我们证明,对于给定的线性波色散关系,该方程组的解与具有相应无色散和线性色散行为的完全可积分方程的拉克斯对准经典极限相关。我们用几个例子来说明这一理论。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Asymptotic integrability of nonlinear wave equations.

We introduce the notion of asymptotic integrability into the theory of nonlinear wave equations. It means that the Hamiltonian structure of equations describing propagation of high-frequency wave packets is preserved by hydrodynamic evolution of the large-scale background wave so that these equations have an additional integral of motion. This condition is expressed mathematically as a system of equations for the carrier wave number as a function of the background variables. We show that a solution of this system for a given dispersion relation of linear waves is related to the quasiclassical limit of the Lax pair for the completely integrable equation having the corresponding dispersionless and linear dispersive behavior. We illustrate the theory with several examples.

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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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