General inverse scattering theory (AKNS) for e.g. sine-Gordon, nonlinear Schrödinger, Korteweg-de Vries equations and discrete systems. Soliton perturbation theory based on variational methods and collective coordinate methods. Coherent structures and chaos. Stochastic perturbations and nonlinear diffusion. Quantization of discrete systems. The derivation of nonlinear partial differential equations for optical fibres and erbium doped fibre amplifiers, long Josephson junctions and long biomolecular systems such as proteins and DNA strings. Inclusion of thermal noise. The classical "Discrete Self Trapping" (DST) equation and other anharmonic lattice equations. Quantization methods. Collapse phenomena in one and two dimensions. Nonlinear models of quantum well lasers and fibre ring lasers to generate ultra short light pulses for optical communications systems.
