相关论文: Integrable Systems and Isomonodromy Deformations
Static axisymmetric Einstein-Maxwell-Dilaton and stationary axisymmetric Einstein-Maxwell-Dilaton-Axion (EMDA) theories in four space-time dimensions are shown to be integrable by means of the inverse scattering transform method. The proof…
For system of two ordinary differential equations of the second order representing autonomous non-conservative holonomic mechanical system, in case of dynamics such as one-frequency periodical oscillations, is found integrated invariant of…
The concept of the nonholonomic deformation formulated recently for the AKNS family is extended to the Kaup-Newell class. Applying this construction we discover a novel two-fold integrable hierarchy related to the deformed derivative…
We prove that matrix Fredholm determinants related to multi-time processes can be expressed in terms of determinants of integrable kernels \`a la Its-Izergin-Korepin-Slavnov (IIKS) and hence related to suitable Riemann-Hilbert problems,…
We construct a family of second-order linear difference equations parametrized by the hypergeometric solution of the elliptic Painlev\'e equation (or higher-order analogues), and admitting a large family of monodromy-preserving…
Generalized indefinite strings provide a canonical model for self-adjoint operators with simple spectrum (other classical models are Jacobi matrices, Krein strings and 2x2 canonical systems). We prove a number of Szeg\H{o}-type theorems for…
The wave functions of quantum Calogero-Sutherland systems for trigonometric case are related to polynomials in l variables (l is a rank of root system) and they are the generalization of Gegenbauer polynomials and Jack polynomials. Using…
We study analytic and geometric properties of Stieltjes and inverse Stieltjes families defined on a separable Hilbert space and establish various minimal representations for them by means of compressed resolvents of various types of linear…
We describe generally deformed Heisenberg algebras in one dimension. The condition for a generalized Leibniz rule is obtained and solved. We analyze conditions under which deformed quantum-mechanical problems have a Fock-space…
A problem list in singularity theory. Most of these problems are related with the algorithmic enumeration of possible topological types of non-discriminant Morsifications of real function singularities, and/or with the Picard--Lefschetz…
In this paper, we study length categories using iterated extensions. We consider the problem of classifying all indecomposable objects in a length category, and the problem of characterizing those length categories that are uniserial. We…
In 1970, Gelfand posed the problem of classifying the indecomposable objects in a representation category equivalent to the principal block of Harish-Chandra modules for $\mathsf{SL}_2(\mathbb{R})$; explicit solutions were obtained by…
A special class of integrable nonlinear differential equations related to A.III-type symmetric spaces and having additional reductions are analyzed via the inverse scattering method (ISM). Using the dressing method we construct two classes…
The Hamiltonian approach to isomonodromic deformation systems is extended to include generic rational covariant derivative operators on the Riemann sphere with irregular singularities of arbitrary Poincar\'e rank. The space of rational…
A Lam\'e connection is a logarithmic $\mathrm{sl}(2,\mathbb C)$-connection $(E,\nabla)$ over an elliptic curve $X:\{y^2=x(x-1)(x-t)\}$, $t\not=0,1$, having a single pole at infinity. When this connection is irreducible, we show that it is…
The integrable structure of the two dimensional superconformal field theory is considered. The classical counterpart of our constructions is based on the $\hat{osp}(1|2)$ super-KdV hierarchy. The quantum version of the monodromy matrix…
We re-address the problem of construction of new infinite-dimensional completely integrable systems on the basis of known ones, and we reveal a working mechanism for such transitions. By splitting the problem's solution in two steps, we…
Different group structures which underline the integrable systems are considered. In some cases, the quantization of the integrable system can be provided with substituting groups by their quantum counterparts. However, some other group…
In this paper, first we introduce the notion of an embedding tensor on a 3-Lie algebra, which naturally induces a 3-Leibniz algebra. Using the derived bracket, we construct a Lie 3-algebra, whose Maurer-Cartan elements are embedding…
In this article, we propose a class of six-dimensional Painleve systems given as the monodromy preserving deformations of the Fuchsian systems. They are expressed as polynomial Hamiltonian systems of sixth order. We also discuss their…