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Abstract <p> The paper studies a wave equation whose velocity has a localized perturbation at some point <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(x_0\)</EquationSource> </InlineEquation>. 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 <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\varepsilon,\)</EquationSource> </InlineEquation> and the width of the localized inhomogeneity is of the order of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\sqrt{\varepsilon},\)</EquationSource> </InlineEquation> where <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\varepsilon\)</EquationSource> </InlineEquation> is a small parameter that tends to 0. </p> <p> <b> DOI</b> 10.1134/S1061920825600400 </p>

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Short-Wave Solutions of the Wave Equation with Localized Velocity Perturbations Whose Wavelength Is Not Comparable to the Scale of Localized Inhomogeneity. One-Dimensional Case

  • 期刊论文

  • 发表日期：

    2025年3月1日

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  • A.I. Allilueva,
  • A.I. Shafarevich

摘要

Abstract

The paper studies 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 \(\sqrt{\varepsilon},\) where \(\varepsilon\) is a small parameter that tends to 0.

DOI 10.1134/S1061920825600400