Cargando…
Integrable systems : twistors, loop groups, and Riemann surfaces : based on lectures given at a conference on integrable systems organized by N.M.J. Woodhouse and held at the Mathematical Institute, University of Oxford, in September 1997 /
This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned exp...
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Otros Autores: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Oxford :
Clarendon Press,
2013.
|
| Colección: | Oxford graduate texts in mathematics ;
4. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Contents; List of contributors; 1 Introduction; Bibliography; 2 Riemann surfaces and integrable systems; 1 Riemann surfaces; 2 Line bundles and sheaves; 3 Vector bundles; 4 Direct images of line bundles; 5 Matrix polynomials and Lax pairs; 6 Completely integrable Hamiltonian systems; Bibliography; 3 Integrable systems and inverse scattering; 1 Solitons and the KdV equation; 2 Classical dynamical systems and integrability; 3 Some classical integrable systems; 4 Formal pseudo-differential operators; 5 Scattering theory; 6 The non-linear Schrodinger equation and its scattering.
- 7 Families of flat connections and harmonic maps8 The KdV equation as an Euler equation; 9 Determinants and holonomy; 10 Local conservation laws; 11 The classical moment problem; 12 Inverse scattering; 13 Loop groups and the restricted Grassmannian; 14 Integrable systems and the restricted Grassmannian; 15 Algebraic curves and the Grassmannian; Bibliography; 4 Integrable Systems and Twisters; 1 General comments on integrable systems; 2 Some elementary geometry; 3 First example: self-dual Yang-Mills; 4 Twistor space and holomorphic vector bundles.
- 5 Yang-Mills-Higgs solitons and minitwistor space6 Generalizations; Bibliography; Index; B; C; D; E; F; G; H; I; J; K; L; M; N; O; P; R; S; T; V; W; Y; Z.