Related papers: On Construction of Recursion Operators From Lax Re…
We elaborate the trigonometric version of intertwining vectors and factorized L-operators. The starting point is the corresponding elliptic construction with Belavin's R-matrix. The naive trigonometric limit is singular and a careful…
A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…
We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…
We give reconstruction formulas inverting the geodesic X-ray transform over functions (call it $I_0$) and solenoidal vector fields on surfaces with negative curvature and strictly convex boundary. These formulas generalize the…
We present the Lax operator for the N=3 KdV hierarchy and consider its extensions. We also construct a new infinite family of N=2 supersymmetric hierarchies by exhibiting the corresponding super Lax operators. The new realization of N=4…
The Lax representation for the nonstationary Schr\"odinger equation with rather arbitrary potential is proposed. Some examples of the construction of exact solutions are given by means of Darboux Transformation method.
Direct and inverse recursion operator is derived for the vacuum Einstein equations for metrics with two commuting Killing vectors that are orthogonal to a foliation by 2-dimensional leaves.
In a recent series of papers by Lou et al., it was conjectured that higher dimensional integrable equations may be constructed by utilizing some conservation laws of (1 + 1)-dimensional systems. We prove that the deformation algorithm…
We construct a new variety of $N=2$ supersymmetric integrable systems by junction of pseudo-differential superspace Lax operators for $a=4$, $N=2$ KdV and multi-component $N=2$ NLS hierarchies. As an important particular case, we obtain Lax…
Recent results on the construction and applications of the transmutation (transformation) operators are discussed. Three new representations for solutions of the one-dimensional Schr\"odinger equation are considered. Due to the fact that…
Using deformations of associative products, derivative nonlinear Schrodinger (DNLS) hierarchies are recovered as AKNS-type hierarchies. Since the latter can also be formulated as Gelfand-Dickey-type Lax hierarchies, a recently developed…
For a fixed root of a quiver, it is a very hard problem to construct all or even only one indecomposable representation with this root as dimension vector. We investigate two methods which can be used for this purpose. In both cases we get…
We propose a method for constructing the Lax connection of two-dimensional relativistic integrable sigma models on coset spaces by means of exponentiation of a suitable operator. We derive a simple quadratic relation that this operator must…
A generalization of the quantum inverse scattering method is proposed replacing the quantum group $RLL$ commutation relations of Lax operators by reflection equation type $RLRL$ commutation relations. Under some natural assumptions the most…
In this paper, we construct a new Lax operator for the elliptic Calogero-Moser model with N=2. The nondynamical r-matrix structure of this Lax operator is also studied . The relation between our Lax operator and the Lax operator given by…
We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic…
We construct an operator system generated by $4$ operators that is not hyperrigid, although all restrictions of irreducible representations have the unique extension property.
We consider the theory of Lax equations in complex simple and reductive classical Lie algebras with the spectral parameter on a Riemann surface of finite genus. Our approach is based on the new objects -- the Lax operator algebras, and…
We study a class of integrable non-linear differential equations related to the A.III-type symmetric spaces. These spaces are realized as factor groups of the form SU(N)/S(U(N-k) x U(k)). We use the Cartan involution corresponding to this…
We describe the representation of arbitrary density operators in terms of expectation values of simple projection operators. Two representations are presented which yield non--recursive schemes for experimentally determining the density…