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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.

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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