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 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