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Reflection and refraction of Lagrangian manifolds corresponding to short-wave solutions of the wave equation with an abruptly varying velocity. (English) Zbl 1468.35033

Summary: In this work, we describe the propagation of waves in media containing localized rapidly changing inhomogeneities (for example, narrow underwater ridges or pycnoclines in ocean, layers with drastically changing optical or acoustic density, etc.).

MSC:

35C20 Asymptotic expansions of solutions to PDEs
35C10 Series solutions to PDEs
35L15 Initial value problems for second-order hyperbolic equations
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