Over the past thirty years significant progress has been made in the investigation of nonlinear waves--including "soliton equations," a class of nonlinear wave equations that arise frequently in such areas as nonlinear optics, fluid dynamics, and statistical physics. The broad interest in this field can be traced to understanding "solitons" and the associated development of a method of solution termed the inverse scattering transform (IST). The IST technique applies to continuous and discrete nonlinear Schrodinger (NLS) equations of scalar and vector type. This work presents a detailed...