HexaKdV

An analog of the lattice KdV equation of Nijhoff et al. is constructed on a hexagonal lattice. The resulting system of difference equations exhibits soliton solutions with interesting local structure: there is a nontrivial phase shift on moving between adjacent lattice sites, with the magnitude of the shift tending to zero in the continuum limit.Comment: LaTeX, 9 pages, 2 figures, see warning at top of fil

The KdV Action and Deformed Minimal Models

An action is constructed that gives an arbitrary equation in the KdV or MKdV hierarchies as equation of motion; the second Hamiltonian structure of the KdV equation and the Hamiltonian structure of the MKdV equation appear as Poisson bracket structures derived from this action. Quantization of this theory can be carried out in two different schemes, to obtain either the quantum KdV theory of Kupershmidt and Mathieu or the quantum MKdV theory of Sasaki and Yamanaka. The latter is, for specific values of the coupling constant, related to a generalized deformation of the minimal models, and clarifies the relationship of integrable systems of KdV type and conformal field theories. As a generalization it is shown how to construct an action for the $SL(3)$-KdV (Boussinesq) hierarchy.Comment: 15 pages, no figures, plain tex. Revised version - a few points clarified. IASSNS-HEP-92/2

Actions for Integrable Systems and Deformed Conformal Theories

I report on work on a Lagrangian formulation for the simplest 1+1 dimensional integrable hierarchies. This formulation makes the relationship between conformal field theories and (quantized) 1+1 dimensional integrable hierarchies very clear.Comment: (based on a talk given at the NSERC-CAP Workshop, "Quantum Groups, Integrable Models and Statistical Systems", Kingston, Ontario, Canada, July 1992), 11 pages, plain tex, no figures, IASSNS-HEP-92/7

Symmetries of KdV and Loop Groups

A simple version of the Segal-Wilson map from the SL(2,C) loop group to a class of solutions of the KdV hierarchy is given, clarifying certain aspects of this map. It is explained how the known symmetries, including Backlund transformations, of KdV arise from simple, field independent, actions on the loop group. A variety of issues in understanding the algebraic structure of Backlund transformations are thus resolved.Comment: 36 pages (sorry), LaTeX using a4 documentstyl

Supersymmetric integrable systems from geodesic flows on superconformal groups

We discuss the possible relationship between geodesic flow, integrability and supersymmetry, using fermionic extensions of the KdV equation, as well as the recently introduced supersymmetrisation of the Camassa-Holm equation, as illustrative examples.Comment: 6 pages, late