Generalization of conserved charges for Toda models

Abstract

The soliton solutions to Toda models receive a zero curvature representation of their equations of motion, i.e. there exist potentials, (Aμ ), that are functional of the fields of the theory and which belong to a Kac-Moody algebra G such that the zero curvature condition is equivalent to the equations of motion. For the construction of the soliton solutions and conserved charges it is required an integer gradation of the Kac-Moody algebra and a “vacuum solution”, such that the potentials evaluated on it belong to an Abelian subalgebra. The conserved charges are then constructed using the dressing method.