41 citations · 158 across the 15 of their papers we have counts for
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Parametric oscillators from factorizations employing a constant-shifted Riccati solution of the harmonic oscillator
H. C. Rosu, K. V. Khmelnytskaya
We determine the kind of parametric oscillators that are generated in the usual factorization procedure of second-order linear differential equations when one introduces a constant…
Spectral parameter power series representation for Hill's discriminant
K. V. Khmelnytskaya, H. C. Rosu
We establish a series representation of the Hill discriminant based on the spectral parameter power series (SPPS) recently introduced by V. Kravchenko. We also show the invariance…
Periodic Sturm-Liouville problems related to two Riccati equations of constant coefficients
K. V. Khmelnytskaya, H. C. Rosu, A. Gonzalez
We consider two closely related Riccati equations of constant parameters whose particular solutions are used to construct the corresponding class of supersymmetrically-coupled seco…
Biquaternions for analytic and numerical solution of equations of electrodynamics
Kira V. Khmelnytskaya, Vladislav V. Kravchenko
We give an overview of recent advances in analysis of equations of electrodynamics with the aid of biquaternionic technique. We discuss both models with constant and variable coeff…
On a quaternionic Maxwell equation for the time-dependent electromagnetic field in a chiral medium
Sergei M. Grudsky, Kira V. Khmelnytskaya, Vladislav V. Kravchenko
Maxwell's equations for the time-dependent electromagnetic field in a homogeneous chiral medium are reduced to a single quaternionic equation. Its fundamental solution satisfying t…
Quaternionic fundamental solutions for the numerical analysis of electromagnetic scattering problems
Kira V. Khmelnytskaya, Vladislav V. Kravchenko, Vladimir S. Rabinovich
We propose a new class of fundamental solutions for the numerical analysis of boundary value problems for the Maxwell equations. We prove completeness of systems of such fundamenta…