M. J. Ablowitz

Discrete and Continuous Nonlinear Schrodinger Systems (eBook, PDF)

• Format: PDF

Produktbeschreibung

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 Schrodinger 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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 24. Dezember 2003
• Englisch
• ISBN-13: 9780511059261
• Artikelnr.: 38205545

Inhaltsangabe

1. Introduction
2. Nonlinear schrödinger equation (NLS)
3. Integrable discrete nonlinear schrödinger equation (IDNSL)
4. Matrix nonlinear Schrödinger equation (MNLS)
5. Integrable discrete matrix NLS equation (IDMNLS)
Appendix A. Summation by parts formula
Appendix B. Transmission of the Jost function through a localized potential
Appendix C. Scattering theory for the discrete Schrödinger equation
Appendix D. Nonlinear Schrödinger systems with a potential term
Appendix E. NLS systems in the limit of large amplitudes.