Factorized Scattering in the Presence of Reflecting Boundaries

We formulate a general set of consistency requirements, which are expected to be satisfied by the scattering matrices in the presence of reflecting boundaries. In particular we derive an equivalent to the boostrap equation involving the W-matrix, which encodes the reflection of a particle off a wall. This set of equations is sufficient to derive explicit formulas for $W$, which we illustrate in the case of some particular affine Toda field theories.