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We construct microlocal parametrices for generic symmetric systems of partial differential equations having characteristics of variable multiplicity. We apply this to obtain microlocal solutions of Cauchy problems for generic classes of electromagnetic and elasto-dynamical systems.
Waves propagating in a medium with highly variable refractive index tend to focus forming caustics. The energy content of the wave field in the vicinity of a caustic is higher than that of the ambient field away from the caustic. Consequently, waves scattering from heterogeneities located near caustics have more energy than a field scattering a little further away from the caustic. For a suitable...
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