Karadzhov Yu. A.
Ukr. Mat. Zh. - 2012. - 64, № 12. - pp. 1641-1640
We consider a special case for curves in two-, three-, and four-dimensional Euclidean spaces and obtain a necessary and sufficient condition for the tensor product surfaces of the planar unit circle centered at the origin and these curves to have a harmonic Gauss map. We present а classification of matrix superpotentials that correspond to exactly solvable systems of Schrodinger equations. Superpotentials of the following form are considered: $W_k = kQ + P \frac 1k$, where $k$ is a parameter and $P, Q$ and $R$ are Hermitian matrices that depend on a variable $x$. The list of three-dimensional matrix superpotentials is explicitly presented.
Singularly perturbed linear boundary-value problems with pulse effects and the regular reduced problem
Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 463–467
A singularly perturbed linear boundary-value problem with pulse effect is considered. By using pseudo-inverse matrices, we construct an asymptotic solution with a single boundary layer.