Construction of Affine and Conformal Affine Toda Solitons by Hirota's Method

TL;DR

This paper constructs new soliton solutions for affine and conformal affine Toda models using Hirota's method, revealing universal mass formulas and exploring specific algebra examples.

Contribution

It introduces a novel recursive scheme and identifies new classes of solitons linked to Cartan matrix degeneracies.

Findings

New classes of solitons connected to Cartan matrix eigenvalue degeneracies

Universal mass formula for Toda solitons

Detailed examples for SU(6) and Sp(3) cases

Abstract

In this talk we report some results about the construction of soliton solutions for the Affine and Conformal Affine Toda models using the Hirota's method. We obtain new classes of solitons connected to the degeneracies of the Cartan matrix eigenvalues as well as to some particular features of the recursive scheme developed here. We obtain an universal mass formula for all those solitons. The examples of $SU(6)$ and $Sp(3)$ are discussed in some detail. ( Talk presented at the VII J.A. Swieca Summer School, Section: Particles and Fields, Campos do Jord\~ao - Brasil - January/93)