Classical backgrounds and scattering for affine Toda theory on a half-line

TL;DR

This paper constructs classical solutions for affine Toda equations with boundary conditions, analyzing soliton scattering and reflection matrices, advancing understanding of integrable models on a half-line.

Contribution

It introduces a method to find classical solutions satisfying boundary conditions using analytically continued solitons, and computes scattering matrices fulfilling bootstrap equations.

Findings

Classical solutions satisfying integrable boundary conditions are obtained.

A large class of classical scattering matrices are calculated.

Scattering matrices satisfy the reflection bootstrap equation.

Abstract

We find classical solutions to the simply-laced affine Toda equations which satisfy integrable boundary conditions using solitons which are analytically continued from imaginary coupling theories. Both static `vacuum' configurations and the time-dependent perturbations about them which correspond to classical vacua and particle scattering solutions respectively are considered. A large class of classical scattering matrices are calculated and found to satisfy the reflection bootstrap equation.