INTEGRABLE HIERARCHIES AND DISPERSIONLESS LIMIT

1994/05/31 by KANEHISA TAKASAKI, Kanehisa Takasaki, TAKASHI TAKEBE +1 · 471 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebra over a field #Hierarchy #Integrable system #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Pure mathematics #Quantization (signal processing) #Toda lattice #Twistor theory #hep-th #nlin.SI #solv-int

paper · pdf · doi:10.1142/s0129055x9500030x

published in Reviews in Mathematical Physics 07(05), 743-808 (World Scientific) · 63 pages, University of Tokyo preprint, UTMS 94-35. (AMS TeX ver.2.1) (Typos are corrected and references are added.)

arxiv created 1994/06/29 · openalex publication_date 1995/07/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 quantization 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.

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