CLASSICAL BACKGROUNDS AND SCATTERING FOR AFFINE TODA THEORY ON A HALF-LINE

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 time-dependent perturbations about them whi ch correspond respectively to classical vacua and particle scattering solutions are considered. A large class of classical scattering matric es are calculated and found to satisfy the reflection bootstrap equati on.