28 citations · 102 across the 11 of their papers we have counts for
12 papers
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…
Spectral parameter power series for arbitrary order linear differential equations
Vladislav V. Kravchenko, R. Michael Porter, Sergii M. Torba
Let be the -th order linear differential operator with variable coefficients. A representation is given for linearly ind…
Spectral problems in inhomogeneous media, spectral parameter power series and transmutation operators
Vladislav V. Kravchenko, Sergii M. Torba
We give a brief overview of recent developments in Sturm-Liouville theory concerning operators of transmutation (transformation) and spectral parameter power series (SPPS) and prop…
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…
Spatial pseudoanalytic functions arising from the factorization of linear second order elliptic operators
Vladislav V. Kravchenko, Sébastien Tremblay
Biquaternionic Vekua-type equations arising from the factorization of linear second order elliptic operators are studied. Some concepts from classical pseudoanalytic function theor…
Solution of boundary value and eigenvalue problems for second order elliptic operators in the plane using pseudoanalytic formal powers
Raul Castillo Perez, Vladislav V. Kravchenko, Rabindranath Resendiz Vazquez
We propose a method for solving boundary value and eigenvalue problems for the elliptic operator D=divpgrad+q in the plane using pseudoanalytic function theory and in particular ps…