The method of Λ-operators developed by S. Derkachov, G. Korchemsky, A. Ma-nashov is applied to a derivation of eigenfunctions for the open Toda chain. The Sklyanin measure is reproduced using diagram technique developed for these Λ-operators. The properties of the Λ-operators are studied. This approach to the open Toda chain eigenfunctions reproduces Gauss-Givental representation for these eige...

We present the q-deformed multivariate hypergeometric functions related to Schur polynomials as tau-functions of the KP and of the two-dimensional Toda lattice hierarchies. The variables of the hypergeometric functions are the higher times of those hierarchies. The discrete Toda lattice variable shifts parameters of hypergeometric functions. The role of additional symmetries in generating hyper...

In this paper, we obtain a generalized BB acklund transformation for the bilinear representation of the two-dimensional Toda lattice equation, in which BB acklund parameters are functions of x, y, n. Furthermore, corresponding nonlinear superposition formula are derived and using these results, we obtain some new explicit solutions of the two-dimensional Toda lattice equation.

The five-dimensional supersymmetric SU(N) gauge theory is studied in the framework of the relativistic Toda chain. This equation can be embedded in two-dimensional Toda lattice hierarchy. This system has the conjugate structure. This conjugate structure corresponds to the charge conjugation.

The algebraic conditions that specific gaugedG/H-WZWmodel have to satisfy in order to give rise to Non-Abelian Toda models with non singular metric with or without torsion are found. The classical algebras of symmetries corresponding to grade one rank 2 and 3 singular NA-Toda models are derived. The proliferation of different two dimensional G0-Toda theories ([2] [10] ) addresses the question a...

1.1. The Toda lattice equation introduced by Toda as a Hamilton equation describing the motion of the system of particles on the line with an exponential interaction between closest neighbours gave rise to numerous important generalizations and helped to discover many of the exciting phenomena in the theory of integrable equations. In Flaschka’s variables [F] the finite non-periodic Toda lattic...

We first summarize features of free, forced and stochastic harmonic oscillations and, following an idea first proposed by Lord Rayleigh in 1883, we discuss the possibility of maintaining them in the presence of dissipation. We describe how phonons appear in a harmonic (linear) lattice and then use the Toda exponential interaction to illustrate solitonic excitations (cnoidal waves) in a one-dime...

Correlation functions of Toda field vertices are investigated by applying the method of integrating zero-mode developed for Liouville theory. We generalize the relations among the zero-, twoand three-point couplings known in Liouville case to arbitrary Toda theories. Twoand three-point functions of Toda vertices associated with the simple roots are obtained. Since the impressive success of Goul...

A Toda equation is specified by a choice of a Lie group and a Z-gradation of its Lie algebra. The Toda equations associated with loop groups of complex classical Lie groups, whose Lie algebras are endowed with integrable Z-gradations with finite dimensional grading subspaces, are described in an explicit form.

We show that the scalar product of the phase model on a finite rectangular lattice is a (restricted) τ -function of the 2-Toda hierarchy. Using this equivalence we then show that the wave-functions of the hierarchy correspond to certain classes of boundary correlation functions of the model. 0. Introduction In [1], it was observed that the N × N domain wall partition function, ZN , of the six v...