Related papers: Construction of solutions of Toda lattices by the …

In 1974 J\"urgen Moser has shown that the classical Moment Problem plays a fundamental role for the theory of completely integrable systems, by proving that the simplest case of the finite Toda lattice is described exhaustively in its…

We study an initial value problem for the Toda lattice with almost periodic initial data. We consider initial data for which the associated Jacobi operator is absolutely continuous and has a spectrum satisfying a Craig-type condition, and…

We develop algebro-geometrical approach for the open Toda lattice. For a finite Jacobi matrix we introduce a singular reducible Riemann surface and associated Baker-Akhiezer functions. We provide new explicit solution of inverse spectral…

We prove that the classical, non-periodic Toda lattice is super-integrable. In other words, we show that it possesses 2N-1 independent constants of motion, where N is the number of degrees of freedom. The main ingredient of the proof is the…

This paper is the continuation of the work "On an inverse problem for finite-difference operators of second order". We consider the Cauchy problem for the Toda lattice in the case when the corresponding L-operator is a Jacobi matrix with…

We find a sequence consisting of time dependent evolution vector fields whose time independent part corresponds to the master symmetries for the Toda equations. Each master symmetry decomposes as a sum consisting of a group symmetry and a…

We give a survey of the long-time asymptotics for the Toda lattice with steplike constant initial data using the nonlinear steepest descent analysis and its extension based on a suitably chosen $g$-function. Analytic formulas for the…

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 construct a new class of positive solutions for a classical semilinear elliptic problem in the plane which arise for instance as the standing-wave problem for the standard nonlinear Schr\"odinger equation or in nonlinear models in…

Using a contraction procedure, we obtain Toda theories and their structures, from affine Toda theories and their corresponding structures. By structures, we mean the equation of motion, the classical Lax pair, the boundary term for half…

We generalize the Toda lattice (or Toda chain) equation to the square lattice; i.e., we construct an integrable nonlinear equation, for a scalar field taking values on the square lattice and depending on a continuous (time) variable,…

We establish relationships between the classical moments problems which are problems of a construction of a measure supported on a real line, on a half-line or on an interval from prescribed set of moments with the Boundary control approach…

Symmetries of the periodic Toda lattice are expresssed in action-angle coordinates and characterized in terms of the periodic and Dirichlet spectrum of the associated Jacobi matrices. Using these symmetries, the phase space of the lattice…

We consider the large number of particles limit of a periodic Toda lattice for a family of initial data close to the equilibrium state. We show that each of the two edges of the spectra of the corresponding Jacobi matrices is up to an…

It has been observed that the dynamics of the Toda lattice can be well described by solutions of the Korteweg-de Vries (KdV) equation in the continuum limit. We show that, under the KdV scaling and a suitable translation, the solution of…

We use the combinatorics of toric networks and the double affine geometric $R$-matrix to define a three-parameter family of generalizations of the discrete Toda lattice. We construct the integrals of motion and a spectral map for this…

We find classical solutions to the simply-laced affine Toda equations which satisfy integrable boundary conditions using solitons which are analytically continued from imaginary coupling theories. Both static `vacuum' configurations and the…

We show how to construct semi-invariants and integrals of the full symmetric sl(n) Toda lattice for all n. Using the Toda equations for the Lax eigenvector matrix we prove the existence of semi-invariants which are homogeneous coordinates…

We introduce a spectral transform for the finite relativistic Toda lattice (RTL) in generalized form. In the nonrelativistic case, Moser constructed a spectral transform from the spectral theory of symmetric Jacobi matrices. Here we use a…

We give an analytic, sufficient condition for the existence of the Backlund transformation between the semiinfinite Toda and Volterra lattices, in the complex case, extending previous results given for the real case.