We present a new realization of scalar integrable hierarchies in terms of the Toda lattice hierarchy. In other words, we show on a large number of examples that an integrable hierarchy, defined by a pseudodifferential Lax operator, can be embedded in the Toda lattice hierarchy. Such a realization in terms the Toda lattice hierarchy seems to be as general as the Drinfeld–Sokolov realization.

An affine Toda-Sutherland system is a quasi-exactly solvable multi-particle dynamics based on an affine simple root system. It is a ‘cross’ between two well-known integrable multi-particle dynamics, an affine Toda molecule and a Sutherland system. Polynomials describing the equilibrium positions of affine Toda-Sutherland systems are determined for all affine simple root systems.

New formulations of the solutions of N=1 and N=2 super Toda field theory are introduced, using Hamiltonian reduction of the N=1 and N=2 super WZNW Models to the super Toda Models. These pa-rameterisations are then used to present the Hamiltonian formulations of the super Toda theories on the spaces of solutions.

We calculate normalization factors and reflection amplitudes in the Winvariant conformal quantum field theories. Using these CFT data we derive vacuum expectation values of exponential fields in affine Toda theories and related perturbed conformal field theories. We apply these results to evaluate explicitly the expectation values of order parameters in the field theories associated with statis...

Abstract. In this paper, we provide a new formulation for the generalized periodic Toda lattice. Since the work of Kostant, Adler and Symes, it has been known that the Toda lattice is related to the structure of simple Lie algebras. Indeed, the non-periodic and the periodic Toda lattices can be expressed as Hamiltonian systems on coadjoint orbits: the former of a simple Lie group and the latter...

An N=(2|2) superfield formulation of the N=(2|2) supersymmetric Toda lattice hierarchy is proposed, and its five real forms are presented. 1. Introduction. Recently the N=(1|1) supersymmetric generalization of the Darboux transformation was proposed in [1], and an infinite class of bosonic and fermionic solutions of its symmetry equation was constructed in [1, 2]. These solutions generate boson...

We show that the Flaschka map, originally introduced to analyze the dynamics of the integrable Toda lattice system, is the inverse of a momentum map. We discuss the geometrical setting of the map and apply it to the generalized Toda lattice systems on semisimple Lie algebras, the rigid body system on Toda orbits, and to coadjoint orbits of semidirect products groups. In addition, we develop an ...

Unexpected relations are found between the Toda lattice, the relativistic Toda lattice and the Bruschi–Ragnisco lattice, as well as between their integrable discretizations.

We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda Lattice hierarchy (2DTL). We also show that the RTC is gauge equivalent to the discrete AKNS hierarchy and the unitary matrix model. Relativistic Toda molecule hierarchy is also considered, along with the forced RTC. The simple approach to the discrete RTC hierarchy based o...

We consider Quantum Toda theory associated to a general Lie algebra. We prove that the conserved quantities in both conformal and affine Toda theories exhibit duality interchanging the Dynkin diagram and its dual, and inverting the coupling constant. As an example we discuss the conformal Toda theories based on B2, B3 and G2 and the related affine theories. Feb 1992 1Email: H G [email protected]....