This book brings together several aspects of soliton theory currently available only in research papers. Emphasis is given to the multi-dimensional problems which arise and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the dbar method.

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...

The theory of solitons involves a broad variety of mathematical methods and appears in many areas of physics, technology, biology, and pure and applied mathematics. In this book, emphasis is placed on both theory (considering mathematical approaches for classical and quantum nonlinear systems -- both continuous and discrete) and experiment (with special discussions on high bit rate optical communications and pulse dynamics in optical materials).

The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg de Vries (KdV) in the nineteenth century. In the 1960s, researchers developed effective asymptotic methods for deriving nonlinear wave equations, such as the KdV equation, governing a broad class of physical phenomena that admit special solutions including those commonly known as solitons. This book describes the underlying approximation techniques and methods for finding solutions to these and other equations. The concepts and methods covered include wave dispersion, asymptotic...