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An analytic method for the initial value problem of the electric field system in vertical inhomogeneous anisotropic media. (English) Zbl 1224.35392
Summary: The time-dependent system of partial differential equations of the second order describing the electric wave propagation in vertically inhomogeneous electrically and magnetically biaxial anisotropic media is considered. A new analytical method for solving an initial value problem for this system is the main object of the paper. This method consists in the following: the initial value problem is written in terms of Fourier images with respect to lateral space variables, then the resulting problem is reduced to an operator integral equation. After that the operator integral equation is solved by the method of successive approximations. Finally, a solution of the original initial value problem is found by the inverse Fourier transform.
35Q60 PDEs in connection with optics and electromagnetic theory
35L55 Higher-order hyperbolic systems
35L15 Initial value problems for second-order hyperbolic equations
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