Discrete and Continuous Nonlinear Schrodinger Systems - Ablowitz, Mark J.

. .

Résumé :
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 Schr? dinger (NLS) equations of scalar and vector type. This work presents a detailed mathematical study of the scattering theory, offers soliton solutions, and analyzes both scalar and vector soliton interactions. The authors provide advanced students and researchers with a thorough and self-contained presentation of the IST as applied to nonlinear Schr? dinger systems.

Sommaire:
1. Introduction; 2. Nonlinear schr?dinger equation (NLS); 3. Integrable discrete nonlinear schr?dinger equation (IDNSL); 4. Matrix nonlinear Schr?dinger 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 Schr?dinger equation; Appendix D. Nonlinear Schr?dinger systems with a potential term; Appendix E. NLS systems in the limit of large amplitudes.