publication . Article . Other literature type . Preprint . 2011

INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT

Takasaki, Kanehisa; Takebe, Takashi;
Open Access
  • Published: 21 Nov 2011 Journal: Reviews in Mathematical Physics, volume 7, pages 743-808 (issn: 0129-055X, eissn: 1793-6659, Copyright policy)
  • Publisher: World Scientific Pub Co Pte Lt
Abstract
Analogues of the KP and the Toda lattice hierarchy called dispersionless KP and Toda hierarchy are studied. Dressing operations in the dispersionless hierarchies are introduced as a canonical transformation, quantization of which is dressing operators of the ordinary KP and Toda hierarchy. An alternative construction of general solutions of the ordinary KP and Toda hierarchy is given as twistor construction which is quatization of the similar construction of solutions of dispersionless hierarchies. These results as well as those obtained in previous papers are presented with proofs and necessary technical details.
Subjects
arXiv: Nonlinear Sciences::Exactly Solvable and Integrable SystemsHigh Energy Physics::Theory
free text keywords: Mathematical Physics, Statistical and Nonlinear Physics, Operator (computer programming), Quantization (signal processing), Canonical transformation, Hierarchy, Integrable system, Mathematics, Toda lattice, Mathematical proof, Twistor theory, Algebra, Mathematical analysis, High Energy Physics - Theory, Nonlinear Sciences - Exactly Solvable and Integrable Systems
Related Organizations

[1] Takasaki, K., and Takebe, T., SDiff(2) KP hierarchy, in: Proceedings of RIMS Research Project 1991 “Infinite Analysis,” Int. J. Mod. Phys. A7, Suppl. 1B (1992), 889-922.

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