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The fundamental solution of the time-dependent system of crystal optics. (English) Zbl 1160.78001
Fundamental solution of the Maxwell equations describing propagation of electromagnetic waves in an anisotropic medium with a constant magnetic permeability is constructed using the Herglotz-Petrovskii representation. This technique allows expressing the solution of initial-value Cauchy problem for the electric vector in terms of integrals over real loops. Non-propagating term corresponding to the mode with zero wave speed is introduced without derivation. Graphical representation of the solutions evaluated numerically is given.

MSC:
78A40 Waves and radiation in optics and electromagnetic theory
35L15 Initial value problems for second-order hyperbolic equations
35Q60 PDEs in connection with optics and electromagnetic theory
35C15 Integral representations of solutions to PDEs
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