11 citations · 18 across the 5 of their papers we have counts for
5 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 method for discontinuous coefficients
Herminio Blancarte, Hugo M. Campos, Kira V. Khmelnytskaya
Let (a,b) be a finite interval and 1/p, q, r be functions from L1(a,b). We show that a general solution (in the weak sense) of the equation (pu')'+qu = zru on (a,b) can be construc…
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…
Bloch Solutions of Periodic Dirac Equations in SPPS Form
K. V. Khmelnytskaya, H. C. Rosu
We provide the representation of quasi-periodic solutions of periodic Dirac equations in terms of the spectral parameter power series (SPPS) recently introduced by V.V. Kravchenko…
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…