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

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