Related papers: Transition function for the Toda chain model
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…
We consider Baxter Q-operators for various versions of quantum affine Toda chain. The interpretation of eigenvalues of the finite Toda chain Baxter operators as local Archimedean L-functions proposed recently is generalized to the case of…
An effective method for constructing explicit solutions to the Davey--Stewartson type integrable equations is discussed based on the use of a dressing chain. The application of the method is exemplified by the equation DS I, for which a new…
In this paper we study Steklov eigenvalues for the Lam\'e operator which arise in the theory of linear elasticity. In this eigenproblem the spectral parameter appears in a Robin boundary condition, linking the traction and the displacement.…
We extend a recent result of [13] for the KdV hierarchy to the Toda lattice hierarchy. Namely, for an arbitrary solution to the Toda lattice hierarchy, we define a pair of wave functions, and use them to give explicit formulae for the…
In this paper we study spectral properties of Dirichlet-to-Neumann map on differential forms obtained by a slight modification of the definition due to Belishev and Sharafutdinov. The resulting operator $\Lambda$ is shown to be self-adjoint…
We conjecture an explicit construction of integral operators intertwining various quantum Toda chains. Compositions of the intertwining operators provide recursive and Q-operators for quantum Toda chains. In particular we propose a…
We propose integral representations for wave functions of B_n, C_n, and D_n open Toda chains at zero eigenvalues of the Hamiltonian operators thus generalizing Givental representation for A_n. We also construct Baxter Q-operators for closed…
In arXiv:1306.2914 a method for approximate solution of Sturm-Liouville equations and related spectral problems was presented based on the construction of the Delsarte transmutation operators. The problem of numerical approximation of…
We introduce a new method for analyzing midpoint discretizations of stochastic differential equations (SDEs), which are frequently used in Markov chain Monte Carlo (MCMC) methods for sampling from a target measure $\pi \propto \exp(-V)$.…
We consider the quantum Toda chain using the method of separation of variables. We show that the matrix elements of operators in the model are written in terms of finite number of ``deformed Abelian integrals''. The properties of these…
A general Casoratian formulation is proposed for the 2D Toda lattice equation, which involves coupled eigenfunction systems. Various Casoratian type solutions are generated, through solving the resulting linear conditions and using a…
A connection between the semigroup of the Cauchy process killed upon exiting a domain $D$ and a mixed boundary value problem for the Laplacian in one dimension higher known as the "mixed Steklov problem," was established in a previous paper…
We apply the Separation of Variables method to obtain eigenvectors of commuting Hamiltonians in the quantum relativistic Toda chain at a root of unity with boundary interaction.
We apply an analogue of the Zakharov-Shabat dressing method to obtain infinite matrix solutions to the Toda lattice hierarchy. Using an operator transformation we convert some of these into solutions in terms of integral operators and…
The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of…
We use the eigenfunction method to calculate the Clebsh-Gordan coefficients for the permutation group . This method is well-established by Jin-Quan Chen. Here we elaborate the detailed procedures for the pedagogical purpose. Due to the…
Originally a model for wave propagation on the line, the Toda lattice is a wonderful case study in mechanics and symplectic geometry. In Flaschka's variables, it becomes an evolution given by a Lax pair on the vector space of real,…
We study analytically the behavior of the largest Lyapunov exponent $\lambda_1$ for a one-dimensional chain of coupled nonlinear oscillators, by combining the transfer integral method and a Riemannian geometry approach. We apply the results…
General Lagrangian theory of discrete one-dimensional integrable systems is illustrated by a detailed study of B\"acklund transformations for Toda-type systems. Commutativity of B\"acklund transformations is shown to be equivalent to…