Discrete and Continuous Nonlinear Schrödinger Systems (London Mathematical Society Lecture Note Series)

Ablowitz, M. J./ Prinari, B./ Trubatch, A. D.

Cambridge University Press（2003/12発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 268 p.
• 言語 ENG
• 商品コード 9780521534376
• DDC分類 515.355

Full 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.

Contents

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.