28 citations · 102 across the 11 of their papers we have counts for
6 papers · 1 filter
Time-dependent one-dimensional electromagnetic wave propagation in inhomogeneous media: exact solution in terms of transmutations and Neumann series of Bessel functions
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…
Eigenvalue problems, spectral parameter power series, and modern applications
K. V. Khmelnytskaya, V. V. Kravchenko, H. C. Rosu
In the present review we deal with the recently introduced method of spectral parameter power series (SPPS) and show how its application leads to an explicit form of the characteri…
Zakharov-Shabat system and hyperbolic pseudoanalytic function theory
Viktor G. Kravchenko, Vladislav V. Kravchenko, Sébastien Tremblay
In [1] a hyperbolic analogue of pseudoanalytic function theory was developed. In the present contribution we show that one of the central objects of the inverse problem method the…
On the Klein-Gordon equation and hyperbolic pseudoanalytic function theory
Vladislav Kravchenko, Dominic Rochon, Sebastien Tremblay
Elliptic pseudoanalytic function theory was considered independently by Bers and Vekua decades ago. In this paper we develop a hyperbolic analogue of pseudoanalytic function theory…
On the solution of the static Maxwell system in axially symmetric inhomogeneous media
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Hector Oviedo
We consider the static Maxwell system with an axially symmetric dielectric permittivity and construct complete systems of its solutions which can be used for analytic and numerical…
An analogue of the Sommerfeld radiation condition for the Dirac operator
Vladislav V. Kravchenko, Raul Castillo P
A simple radiation condition at infinity for time-harmonic massive Dirac spinors is proposed. This condition allows an analogue of the Cauchy integral formula in unbounded domains…