Short-Wave Asymptotic Solutions of the Wave Equation with Localized Velocity Perturbations Whose Wavelength is not Comparable to the Scale of the Localized Inhomogeneity.
Anna Ivanovna Allilueva, А. И. Шафаревич · Russian Journal of Mathematical Physics · 2025
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