In any 2-category C with zeros (for example the topological 2-category T op∗ of based spaces, based maps and track classes of homotopies) box bracket operations have been defined and studied by Hardie-Marcum-Oda [4]. These are secondary homotopy operations and if (as we will suppose) C admits a suspension functor Σ (see [3]) they take values in morphism groups HC(ΣW,X), here denoted π(ΣW,X), of...

We apply the method of angular quantization to calculation of the wave function renormalization constants in D (1) l affine Toda quantum field theories. A general formula for the wave function renormalization constants in ADE Toda field theories is proposed. We also calculate all one-particle form factors and some of the two-particle form factors of an exponential field. August, 1998 ∗ e-mail a...

We prove that a certain sequence of tau functions of the Garnier system satisfies Toda equation. We construct a class of algebraic solutions of the system by the use of Toda equation; then show that the associated tau functions are expressed in terms of the universal character, which is a generalization of Schur polynomial attached to a pair of partitions. This article is based on the results i...

Quantum canonical transformations are used to derive the integral representations and Kummer solutions of the confluent hypergeometric and hypergeometric equations. Integral representations of the solutions of the non-periodic three body Toda equation are also found. The derivation of these representations motivate the form of a two-dimensional generalized hypergeometric equation which contains...

Resonance and web structure in discrete soliton systems: the two-dimensional Toda lattice and its fully discrete and ultra-discrete versions Abstract. We present a class of solutions of the two-dimensional Toda lattice equation, its fully discrete analogue and its ultra-discrete limit. These solutions demonstrate the existence of soliton resonance and web-like structure in discrete integrable s...

We construct the classical W -algebras for some non-abelian Toda systems associated with the Lie groups GL 2n(R) and Spn(R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian counterparts. The convenient block matrix representation for the Toda equations is used. The infinitesimal symmetry transformations generated by the elements ...

In this article we prove that for locally defined singular SU(n+1) Toda systems in R2, the profile of fully bubbling solutions near the singular source can be accurately approximated by global solutions. The main ingredients of our new approach are the classification theorem of Lin-Wei-Ye [22] and the non-degeneracy of the linearized Toda system [22], which make us overcome the difficulties tha...

We propose affine Toda field theories related to the non-crystallographic Coxeter groups H2, H3 and H4. The classical mass spectrum, the classical three-point couplings and the one-loop corrections to the mass renormalisation are determined. The construction is carried out by means of a reduction procedure from crystallographic to non-crystallographic Coxeter groups. The embedding structure exp...

We establish unique continuation for various discrete nonlinear wave equations. For example, we show that if two solutions of the Toda lattice coincide for one lattice point in some arbitrarily small time interval, then they coincide everywhere. Moreover, we establish analogous results for the Toda, Kac–van Moerbeke, and Ablowitz–Ladik hierarchies. Although all these equations are integrable, t...

The technique of Darboux transformation is applied to nonlocal partner of two–dimensional periodic A n−1 Toda lattice. This system is shown to admit a representation as the compatibility conditions of direct and dual overdetermined linear systems with quantized spectral parameter. The generalization of the Darboux transformation technique on linear equations of such a kind is given. The solutio...