arXiv subjects

Stanislav Spichak

Publications and source records attributed to Stanislav Spichak.

3 recordsLinked to original sources

arXiv2018

Classification of Realizations of Lie Algebras of Vector Fields on a Circle

Finite-dimensional subalgebras of a Lie algebra of smooth vector fields on a circle, as well as piecewise-smooth global transformations of a circle on itself, are considered. A canonical forms of realizations of two- and three-dimensional noncommutative algebras are obtained. It is shown that all other realizations of smooth vector fields are reduced to this form using global transformations. Some combinatorial formulas for the number of inequivalent realizations of these algebras are obtained.

math.RT↗

arXiv2018

Group classification of a class of generalized nonlinear Kolmogorov equations and exact solutions

A class of generalized nonlinear Kolmogorov equations is investigated. We present the group classification of Lie symmetries of the class with respect to the group of equivalence transformations. We find a number of exact solutions of nonlinear Kolmogorov equations which has the maximal symmetry properties.

math.AP↗

arXiv1998

Hermitian quasi-exactly solvable matrix Shroedinger operators

We construct six multi-parameter families of Hermitian quasi-exactly solvable matrix Schroedinger operators in one variable. The method for finding these operators relies heavily upon a special representation of the Lie algebra o(2,2) whose representation space contains an invariant finite-dimensional subspace. Besides that we give several examples of quasi-exactly solvable matrix models that have square-integrable eigenfunctions. These examples are in direct analogy with the quasi-exactly solvable scalar Schroedinger operators obtained by Turbiner and Ushveridze.

math-ph↗