In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called ‘solitons’ and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such ‘soliton equations’. The IST technique applies to both continuous and discrete nonlinear Schrödinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the previously-published literature. • Solution of class of physically interesting nonlinear Schrödinger (NLS) equations • Fills important gap in field literature, covering nonlinear Schrödinger systems and discrete soliton systems in mathematical detail • Careful, concrete and systematic analysis of key aspects of NLS vector soliton interactions.

Discrete and Continuous Nonlinear Schrodinger Systems

PRINARI, Barbara;
2004-01-01

Abstract

In recent years there have been important and far reaching developments in the study of nonlinear waves and a class of nonlinear wave equations which arise frequently in applications. The wide interest in this field comes from the understanding of special waves called ‘solitons’ and the associated development of a method of solution to a class of nonlinear wave equations termed the inverse scattering transform (IST). Before these developments, very little was known about the solutions to such ‘soliton equations’. The IST technique applies to both continuous and discrete nonlinear Schrödinger equations of scalar and vector type. Also included is the IST for the Toda lattice and nonlinear ladder network, which are well-known discrete systems. This book presents the detailed mathematical analysis of the scattering theory; soliton solutions are obtained and soliton interactions, both scalar and vector, are analyzed. Much of the material is not available in the previously-published literature. • Solution of class of physically interesting nonlinear Schrödinger (NLS) equations • Fills important gap in field literature, covering nonlinear Schrödinger systems and discrete soliton systems in mathematical detail • Careful, concrete and systematic analysis of key aspects of NLS vector soliton interactions.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11587/112852
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