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  3. Discrete and Continuous Nonlinear Schrödinger Systems
  • Cited by 165
Publisher:
Cambridge University Press
Online publication date:
October 2009
Print publication year:
2003
Online ISBN:
9780511546709
DOI:
https://doi.org/10.1017/CBO9780511546709
Subjects:
Mathematics (general), Mathematics, Differential and Integral Equations, Dynamical Systems and Control Theory, Mathematical Physics
Series:
London Mathematical Society Lecture Note Series (302)
Information

Book description

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, first published in 2003, 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.

Reviews

'… this valuable book provides a detailed and self-contained presentation of an extremely important tool used in the study of NLS systems.'

Source: EMS Newsletter

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