Maria Filipkovska

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

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...

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,...

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...

The author’s name should read M. S. Filipkovska.

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...

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...

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...

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...

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...