The development and application of collective coordinate theories for soliton equations in external fields, especially non-linear Schrödinger-, Klein-Gordon- and Dirac-type equations. The relationship between these theories and experiments in paramagnetic colloids in the presence of extreme magnetic fields.

The characterisation of Ratchet-type directed transport induced by temporary forces or asymmetric periodic potentials via the symmetries of physical systems and the functional representation between the cause and effect of this phenomenon. Application of this theory to the movement of fluxons in Josephson junctions and the atoms in optical networks and Bose-Einstein condensates.