相关论文: An Integral Operator Solution to the Matrix Toda E…

The Jacobi matrices with bounded elements whose spectrum of multiplicity 2 is separated from its simple spectrum and contains an interval of absolutely continuous spectrum are considered. A new type of spectral data, which are analogous for…

We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…

We present an elementary derivation of the soliton-like solutions in the $A_n^{(1)}$ Toda models which is alternative to the previously used Hirota method. The solutions of the underlying linear problem corresponding to the N-solitons are…

We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional…

The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…

Consequences of the Toda equations arising from the conjectural matrix model for the Riemann sphere are investigated. The Toda equations determine the Gromov-Witten descendent potential (including all genera) of the Riemann sphere from the…

In this report the emphasis is on an alternative representation of the Magnus series by proper operator (matrix) exponential solutions to differential equations (systems), both linear and nonlinear ODEs and PDEs. The main idea here is in…

We show that Toda lattices with the exceptional Cartan matrices are Liouville type systems. For these systems of equations, we obtain explicit formulas for the invariants and generalized Laplace invariants.

The main goal of this paper is to propose an approach to inverse spectral problems for functional-differential operators (FDO) with involution. For definiteness, we focus on the second-order FDO with involution-reflection. Our approach is…

We consider equations that represent a constancy condition for a 2D Wronskian, mixed Wronskian-Casoratian and 2D Casoratian. These determinantal equations are shown to have the number of independent integrals equal to their order - this…

In this paper we express some simple random tensor models in a Givental-like fashion i.e. as differential operators acting on a product of generic 1-Hermitian matrix models. Finally we derive Hirota's equations for these tensor models. Our…

We provide Fredholm conditions for compatible differential operators on certain Lie manifolds (that is, on certain possibly non-compact manifolds with nice ends). We discuss in more detail the case of manifolds with cylindrical, hyperbolic,…

We recover the Tutte polynomial of a matroid, up to change of coordinates, from an Ehrhart-style polynomial counting lattice points in the Minkowski sum of its base polytope and scalings of simplices. Our polynomial has coefficients of…

This paper is a continuation of the work on unbounded Toeplitz-like operators $T_\Om$ with rational matrix symbol $\Om$ initiated in Groenewald et. al (Complex Anal. Oper. Theory 15, 1(2021)), where a Wiener-Hopf type factorization of $\Om$…

We consider four combinatorial interpretations for the algebra of Boolean differential operators. We show that each interpretation yields an explicit matrix representation for Boolean differential operators.

This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continuous. A characteristic property of this class of equations,…

We suggest the procedure of the construction of Baxter Q-operators for Toda chain . Apart from the one-paramitric family of Q-operators, considered in our recent paper (hep-th/9908179) we also give the construction of two basic Q-operators…

In this paper, we investigate approximate solutions for nonlinear Fredholm integro-differential equations of fractional order. We present an operational Tau method by obtaining the Tau matrix representation. We solve a special class of…

Matrix elements of quantum intertwiner as well as the modified Q-operator for the quantum relativistic Toda chain at root of unity are constructed explicitly. Modified Q-operators make isospectrality transformations of quantum transfer…

In this article, we consider a system of integro-differential equations in L^2(R, R^N), which contains the logarithmic Laplacian in the presence of transport terms. The linear operators associated with the system satisfy the Fredholm…