Integrability, self-duality, and twistor theory

L.J. Mason and N.M.J. Woodhouse

It has been known for some time that many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection (for example, the Korteweg-de Vries and nonlinear Schr odinger equations are reductions of the self-dual Yang-Mills equation). This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It has two central themes: first, that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and second that twistor theory provides a uniform geometric framework for the study of B acklund tranformations, the inverse scattering method, and other such general constructions of integrability theory, and that it elucidates the connections between them.

「Nielsen BookData」より

[目次]

  • PART I: SELF-DUALITY AND INTEGRABLE EQUATIONS
  • 1. Mathematical background
  • 2. The self-dual Yang-Mills equations
  • 3. Symmetries and reduction
  • 4. Reductions to three dimensions
  • 5. Reductions to two dimensions
  • 6. Reduction to one dimension
  • 7. Hierarchies
  • 8. Other self-duality equations
  • PART II: TWISTOR THEORY
  • 9. Mathematical background
  • 10. Twistor space and the ward construction
  • 11. Reductions of the ward construction
  • 12. Generalizations of the twistor construction
  • 13. Boundary conditions
  • 14. Construction of exact solutions
  • Appendix A. 1 Lifts and invariant connections
  • Appendix B. 2 Active and passive guage transformations
  • Appendix A. 3 The Drinfeld-Sokolov equations

「Nielsen BookData」より

この本の情報

書名 Integrability, self-duality, and twistor theory
著作者等 Mason, L. J.
Woodhouse, N. M. J.
Woodhouse Nicholas
Mason L.J.
シリーズ名 London Mathematical Society monographs
出版元 Clarendon Press
刊行年月 1996
ページ数 x, 364 p.
大きさ 25 cm
ISBN 9780198534983
NCID BA27738145
※クリックでCiNii Booksを表示
言語 英語
出版国 イギリス
この本を: 
このエントリーをはてなブックマークに追加

このページを印刷

外部サイトで検索

この本と繋がる本を検索

ウィキペディアから連想