Maria Filipkovska

Maria Filipkovska
B.Verkin Institute for Low Temperature Physics and Engineering · Department of Mathematical Physics

Doctor of Philosophy

About

14
Publications
426
Reads
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23
Citations
Citations since 2017
13 Research Items
23 Citations
201720182019202020212022202301234567
201720182019202020212022202301234567
201720182019202020212022202301234567
201720182019202020212022202301234567

Publications

Publications (14)
Preprint
We consider the problem of the propagation of electric field generated by periodic pumping in a stable medium of two-level atoms as the initial-boundary value problem (mixed problem) for the Maxwell-Bloch equations with an arbitrary inhomogeneous broadening. An approach to the study of such a problem is proposed. We use the inverse scattering trans...
Preprint
Two combined numerical methods for solving time-varying semilinear differential-algebraic equations (DAEs) are obtained. These equations are also called degenerate DEs, descriptor systems, operator-differential equations and DEs on manifolds. The convergence and correctness of the methods are proved. When constructing methods we use, in particular,...
Article
Full-text available
We consider the problem of the propagation of an electric field generated by periodic pumping in a stable medium of two-level atoms as the mixed problem for the Maxwell–Bloch equations without spectrum broadening. An approach to the study of such a problem is proposed. We use the inverse scattering transform method in the form of the matrix Riemann...
Article
We consider an irregular (singular) semilinear differential-algebraic equation \( \frac{d}{dt}\left[ Ax\right]+ Bx=f\left(t,x\right) \) and prove the theorems on Lagrange stability and instability. These theorems give sufficient conditions for the existence, uniqueness, and boundedness of the global solution to the Cauchy problem for a semilinear d...
Preprint
Full-text available
Two combined numerical methods for solving semilinear differential-algebraic equations (DAEs) are obtained and their convergence is proved. The comparative analysis of these methods is carried out and conclusions about the effectiveness of their application in various situations are made. In comparison with other known methods, the obtained methods...
Article
Full-text available
We study a semilinear differential-algebraic equation (DAE) with the focus on the Lagrange stability (instability). The conditions for the existence and uniqueness of global solutions (a solution exists on an infinite interval) of the Cauchy problem, as well as conditions of the boundedness of the global solutions, are obtained. Furthermore, the ob...
Article
Full-text available
A mixed initial-boundary value problem for nonlinear Maxwell-Bloch (MB) equations without spectral broadening is studied by using the inverse scattering transform in the form of the matrix Riemann-Hilbert (RH) problem. We use transformation operators whose existence is closely related with the Goursat problems with nontrivial characteristics. We al...
Article
The system of differential-algebraic equations which in a vector form has the representation as the semilinear differential-algebraic equation (DAE) d/dt [Ax(t)]+Bx(t)=f(t,x) with a singular characteristic operator pencil is considered. In particular, underdetermined and overdetermined systems of the differential-algebraic equations correspond to t...

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