Solitons: Differential Equations, Symmetries and Infinite Dimensional AlgebrasCambridge University Press, 2000 - 108 Seiten This book investigates the high degree of symmetry that lies hidden in integrable systems. To that end, differential equations arising from classical mechanics, such as the KdV equation and the KP equations, are used here by the authors to introduce the notion of an infinite dimensional transformation group acting on spaces of integrable systems. Chapters discuss the work of M. Sato on the algebraic structure of completely integrable systems, together with developments of these ideas in the work of M. Kashiwara. The text should be accessible to anyone with a knowledge of differential and integral calculus and elementary complex analysis, and it will be a valuable resource to both novice and expert alike. |
Inhalt
Exercises to Chapter 1 | 9 |
Exercises to Chapter 2 | 18 |
Exercises to Chapter 3 | 31 |
Exercises to Chapter 4 | 41 |
Exercises to Chapter 5 | 52 |
Exercises to Chapter 7 | 66 |
Exercises to Chapter 9 | 87 |
| 103 | |
Andere Ausgaben - Alle anzeigen
Solitons: Differential Equations, Symmetries and Infinite Dimensional Algebras T. Miwa,M. Jimbo,E. Date Keine Leseprobe verfügbar - 2012 |
Häufige Begriffe und Wortgruppen
affine Lie algebra annihilation operators anticommutator bilinear identity black stone Boson-Fermion correspondence Bosonic Bosonic Fock space called charge and energy Clifford algebra coefficients commutation relations commutator bracket conformal field theory consider creation operators defined definition determined differential equation differential operator dimensional vector subspace element evolution equation example Exercises to Chapter Ə² Fermions Fock space formula g|vac gives Grass(m Grassmannian half-integers Hirota derivative Hirota equation Hirota form infinite dimensional infinitesimal transformations integrable system k₁ KdV equation KP equation KP hierarchy lemma m₁ matrix monomial n-soliton solution n₁ nondegenerate nonlinear nonzero normal product notation number of tiles obtained orbit Plücker coordinates Plücker relations projective space Proof prove pseudodifferential operator quadratic expressions representation right-hand side satisfying symmetries tau function transformation group variables x1 vector space vertex operators w₁ Wick's theorem write Young diagram ди მე მთ
Beliebte Passagen
Seite 104 - Deformations of conformal field theories and soliton equations, Phys. Lett. B 224 (1989), 373 22.
Seite 103 - Phys. 25 (1992) 89-101 4. VG Drinfeld and VV Sokolov, "Lie Algebras and Equations of Korteweg-de Vries Type", J.
Seite 104 - Feigin, and E. Frenkel, Free field resolutions in affine Toda field theories Phys. Lett.
Verweise auf dieses Buch
Stochastic Analysis and Mathematical Physics (SAMP/ANESTOC 2002 ... Richard Phillips Feynman,Rolando Rebolledo,Jorge Rezende Eingeschränkte Leseprobe - 2004 |