Solitons, Nonlinear Evolution Equations and Inverse Scattering
Solitons, Nonlinear Evolution Equations and Inverse Scattering
$174.00
USDSolitons 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.
- Ablowitz is one of the founders of soliton theory
- Soliton theory is one of the new growth areas in mathematics, one of the most important ways of solving partial differential equations
- Soliton books sell
Reviews & endorsements
"...well-written and presented." R. Grimshaw, Journal of Fluid Mechanics
"For researchers working in this [field] this book is a valuable source of information which provides an excellent overview of the established results and the present developments. The presentation is clear and well structured, so that novices wishing to move into inverse scattering and solitons will find this book to be a useful introduction to these modern techniques." Walter Oevel, Mathematical Reviews
"...reflects the changing emphasis of current research into solitons and integrable systems by concentrating on systems with more than one space dimension....valuable in bridging the diverse approaches to the subject by analysts and algebraic geometers. It records the relationships between results of gauge theory, Lie algebras and functional analysis and those of classical and numerical analysis....a well-ordered treasure house of ancient and modern work on integrable systems, fascinating and useful to browse in...essential for all specialists on integrable systems and for all major mathematical libraries." P.G. Drazin, Bulletin of the London Mathematical Society
Product details
January 1992Paperback
9780521387309
532 pages
229 × 152 × 34 mm
0.784kg
58 b/w illus. 1 table
Available
Table of Contents
- 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.
