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math.AP2014★ 5 cited
Modulated electromagnetic fields in inhomogeneous media, hyperbolic pseudoanalytic functions and transmutations
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Sergii M. Torba
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 bico…
math.AP2013
P-adic Elliptic Quadratic Forms, Parabolic-Type Pseudodifferential Equations With Variable Coefficients, and Markov Processes
O. F. Casas-Sánchez, W. A. Zúñiga-Galindo
In this article we study the Cauchy problem for a new class of parabolic-type pseudodifferential equations with variable coefficients for which the fundamental solutions are transi…
math.AP2012★ 21 cited
Wave polynomials, transmutations and Cauchy's problem for the Klein-Gordon equation
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Sergii M. Torba +1
We prove a completeness result for a class of polynomial solutions of the wave equation called wave polynomials and construct generalized wave polynomials, solutions of the Klein-G…