Short-Wave Asymptotic Solutions of the Wave Equation with Localized Velocity Perturbations Whose Wavelength is not Comparable to the Scale of the Localized Inhomogeneity.

IF 1.5 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL

Russian Journal of Mathematical Physics Pub Date : 2025-07-29 DOI:10.1134/S1061920825600916

A.I. Allilueva, A.I. Shafarevich

引用次数: 0

Abstract

In this paper we study a wave equation whose velocity has a localized perturbation at some point \(x_0\). The initial condition has the form of a rapidly oscillating wave packet whose wavelength is not comparable with the scale of the inhomogeneity. In this case, the length of the initial wave is of the order of \(\varepsilon\), and the width of the localized inhomogeneity is of the order of \(\varepsilon^{1/m},\) where \(\varepsilon\) is a small parameter that tends to 0, and \(m\) is a positive integer greater than 2.

DOI 10.1134/S1061920825600916

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波长与局域非均匀性尺度不可比的局域速度扰动波动方程的短波渐近解。

本文研究了速度在某一点\(x_0\)有局域摄动的波动方程。初始条件具有快速振荡波包的形式，其波长与非均匀性的尺度不可比较。在这种情况下，初始波的长度为\(\varepsilon\)阶，局域非均匀性的宽度为\(\varepsilon^{1/m},\)阶，其中\(\varepsilon\)是一个趋向于0的小参数，\(m\)是一个大于2的正整数。Doi 10.1134/ s1061920825600916

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Journal of Mathematical Physics 物理-物理：数学物理

CiteScore

3.10

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.