Advanced Series in Mathematical Physics - Vol. 25
BASIC METHODS OF SOLITON THEORY
by Ivan Cherednik (University of North Carolina, USA)
In the 25 years of its existence Soliton Theory has drastically expanded our understanding of "integrability" and contributed a lot to the reunification of Mathematics and Physics in the range from deep algebraic geometry and modern representation theory to quantum field theory and optical transmission lines.
The book is a systematic introduction to the Soliton Theory with an emphasis on its background and algebraic aspects. It is the first one devoted to the general matrix soliton equations, which are of great importance for the foundations and the applications.
Differential algebra (local conservation laws, Bäcklund–Darboux transforms), algebraic geometry (theta and Baker functions), and the inverse scattering method (Riemann–Hilbert problem) with well-grounded preliminaries are applied to various equations including principal chiral fields, Heisenberg magnets, Sin–Gordon, and Nonlinear Schrödinger equation.
Contents:
- Introduction:
- Chiral Fields and Sin–Gordon
Equation
- Generalized Heisenberg Magnet and VNS Equation
- Conservation Laws and Algebraic–Geometric Solutions:
- Local Conservation Laws
- Generalized Lax Equations
- Algebraic-Geometric Solutions of Basic Equations
- Algebraic–Geometric Solutions of Sin-Gordon, NS, etc
- Bäcklund Tranforms and Inverse Problem:
- Bäcklund Transformations
- Introduction to the Scattering Theory
- Applications of the Inverse Problem Method
Readership: Mathematicians, mathematical physicists and graduate students
familiar with basic notions from analysis and algebraic geometry.
"The book is of clear interest for mathematicians, mathematical physicists and graduate students who would like to specialize in the field, and also to those who just want to expand their views on the modern methods in soliton theory."
| 264pp |
Pub. date: Aug 1996 |
This is a Print On Demand title. We no longer stock the original but will recreate a copy for you. While all efforts are made to ensure that quality is the same as the original, there may be differences in some areas of the design and packaging.
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