Modulated electromagnetic fields in inhomogeneous media, hyperbolic   pseudoanalytic functions and transmutations
  The time-dependent Maxwell system describing electromagnetic wave propagation in inhomogeneous isotropic media in the one-dimensional case reduces to a Vekua-type equation for bicomplex-valued functions of a hyperbolic variable (see arXiv:1001.0552). Using this relation we solve the problem of the transmission through an inhomogeneous layer of a normally incident electromagnetic time-dependent plane wave. The solution is written in terms of a pair of Darboux-associated transmutation operators (see arXiv:1111.4449), and combined with the recent results on their construction (see arXiv:1208.6166, arXiv:1306.2914) can be used for efficient computation of the transmitted modulated signals. We develop the corresponding numerical method and illustrate its performance with examples. 
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Sergii M. Torba
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