Momentum conserving defects in affine Toda field theory

This thesis expands previous work on defects appearing in classical integrable field theories, with a generalised form for momentum conserving defects being found. It is shown that the defect equations can always be augmented to give a Bäcklund transformation for the bulk theory, and new momentum conserving defects are found for the Br and Dr ATFTs. Momentum conservation is shown to be a necessary condition if the system is to have an infinite number of conserved quantities for all defects in ATFTs. The D4 defect in particular is investigated, with the system shown to have a zero curvature representation and soliton-defect interactions being investigated.