Aspects of classical backgrounds and scattering for affine Toda theory on a half-line

TL;DR

This paper investigates classical solutions and boundary conditions in affine Toda theories on a half-line, establishing stability criteria, classifying vacua, and analyzing scattering properties through numerical methods.

Contribution

It provides a comprehensive classification of vacuum configurations and reflection factors for A_r^(1) Toda theories with boundary conditions, extending understanding of integrable boundary phenomena.

Findings

Identified conditions for stable vacua via Bogomolny bounds

Classified vacuum configurations for A_r^(1) theories up to r=5

Analyzed boundary singularities and reflection factors numerically

Abstract

In this paper we study various aspects of classical solutions to the affine Toda equations on a half-line with integrable boundary conditions. We begin by finding conditions that the theory has a stable vacuum by finding a Bogomolny bound on the energy, and analysing the possible singularities of the field at the boundary. Using these constraints and extensive numerical investigations we classify the vacuum configurations and reflection factors for A_r^(1) Toda theories up to r=5.