2 Two-Toda lattice and reductions (Hänkel and Toeplitz) 17 2.1 Two-Toda on Moment Matrices and Identities for τ -Functions 18 2.2 Reduction to Hänkel matrices: the standard Toda lattice and a Virasoro algebra of constraints . . . . . . . . . . . . . . . . . 26 2.3 Reduction to Toeplitz matrices: two-Toda Lattice and an SL(2,Z)algebra of constraints . . . . . . . . . . . . . . . . . . . . . . 29...

A new parameterisation of the solutions of Toda field theory is introduced. In this parameterisation, the solutions of the field equations are real, well-defined functions on space-time, which is taken to be two-dimensional Minkowski space or a cylinder. The global structure of the covariant phase space of Toda theory is examined and it is shown that it is isomorphic to the Hamiltonian phase sp...

The Toda lattice equation is a nonlinear evolutionary differential-difference equation introduced by Toda [1] describing an infinite system of masses on a line that interact through an exponential force which is used to explain the well-known FermiPasta-Ulam phenomenon. It was soon realized that this equation is completely integrable, i.e. admits infinite conserved quantities. It has important ...

Quantum A2-Toda field theory in two dimensions is investigated based on the method of quantizing canonical free field. Toda exponential operators associated with the fundamental weights are constructed to the fourth order in the cosmological constant. This leads us to a conjecture for the exact operator solution. It is well-known that Toda field theories in two dimensions admit exact classical ...

In this paper, we consider solutions of the following (open) Toda system (Toda lattice) for SU(N + 1)

This paper establishes certain existence and classification results for solutions to SU(n) Toda systems with three singular sources at 0, 1, and∞. First, we determine the necessary conditions for such an SU(n) Toda system to be related to an nth order hypergeometric equation. Then, we construct solutions for SU(n) Toda systems that satisfy the necessary conditions and also the interlacing condi...

In this paper, we consider solutions of the following (open) Toda system (Toda lattice) for SU (N + 1)

Since the lightcone self dual spherical membrane, moving in flat target backgrounds, has a direct correspondence with the SU(∞) Nahm equations and the continuous Toda theory, we construct the Moyal deformations of the self dual membrane in terms of the Moyal deformations of the continuous Toda theory. This is performed by using the WeylWigner-Moyal quantization technique of the 3D continuous To...

We generalize the Lax pair and Bäcklund transformations for Toda and N=1 super Toda equations to the case of arbitrary worldsheet background geometry. We use the fact that the Toda equations express constant curvature conditions, which arise naturally from flatness conditions equivalent to the W–gravity equations of motion.

We investigate the spatial asymptotics of decaying solutions of the Toda lattice and show that the asymptotic behavior is preserved by the time evolution. In particular, we show that the leading asymptotic term is time independent. Moreover, we establish infinite propagation speed for the Toda lattice. All results are extended to the entire Toda as well as the Kac–van Moerbeke hierarchy.