Solitons, Nonlinear Evolution Equations and Inverse Scattering

This book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

M. A. Ablowitz (Author), P. A. Clarkson (Author)

9780521387309, Cambridge University Press

Paperback, published 12 December 1991

532 pages, 58 b/w illus. 1 table
22.9 x 15.2 x 3.4 cm, 0.784 kg

'It is valuable in bridging the diverse approaches to the subject by analysts and algebraic geometeers … Their book is a well-ordered treasure-house of ancient and modern work … essential for all specialists on integrable systems and for all major mathematical libraries.' LSM

Solitons have been of considerable interest to mathematicians since their discovery by Kruskal and Zabusky. This book brings together several aspects of soliton theory currently only available in research papers. Emphasis is given to the multi-dimensional problems arising and includes inverse scattering in multi-dimensions, integrable nonlinear evolution equations in multi-dimensions and the ? method. Thus, this book will be a valuable addition to the growing literature in the area and essential reading for all researchers in the field of soliton theory.

1. Introduction
2. Inverse scattering for the Korteweg-de Vries equation
3. General inverse scattering in one dimension
4. Inverse scattering for integro-differential equations
5. Inverse scattering in two dimensions
6. Inverse scattering in multidimensions
7. The Painleve equations
8. Discussion and open problems
Appendix A: Remarks on Riemann-Hilbert problems
Appendix B: Remarks on problems
References
Subject index
Author index.

Subject Areas: Differential calculus & equations [PBKJ]