Hamiltonian structure of Sato's hierarchy of KP equations and a coadjoint orbit of a certain formal Lie group
type: Item
instance of: scholarly article
title: Hamiltonian structure of Sato's hierarchy of KP equations and a coadjoint orbit of a certain formal Lie group
zbMATH Open document ID: 0584.58021
DOI: 10.1007/BF00419926
author: Yoshihide Watanabe
published in: Letters in Mathematical Physics
publication date: 1983-01-01T00:00:00Z
review text: Results are announced, without proofs, on the Hamiltonian structure of the hierarchy of Kadomtsev-Petviashvili equations introduced by \textit{M. Sato} [Random systems and dynamical systems, Proc. Symp., Kyoto 1981, RIMS Kokyuroku 439, 30-46 (1981; Zbl 0507.58029)]. It is stated that these are completely integrable Hamiltonian systems. The Hamiltonians and conserved densities are given. The underlying symplectic manifold is a Kostant-Kirillov coadjoint orbit, which is described.
Mathematics Subject Classification ID: 37J35
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
zbMATH DE Number: 3936028
zbMATH Keywords: Kadomtsev-Petviashvili equations
zbMATH Keywords: completely integrable Hamiltonian systems
zbMATH Keywords: Kostant-Kirillov coadjoint orbit
Wikidata QID: Q115395006
MaRDI profile type: Publication
cites work: On a trace functional for formal pseudo-differential operators and the symplectic structure of the Korteweg-deVries type equations
cites work: Fractional powers of operators and Hamiltonian systems
cites work: Gel'fand-Dikii Hamiltonian operator and the coadjoint representation of the Volterra group
cites work: Algebraic aspects of nonlinear differential equations
cites work: Hamiltonian structure of M. Sato's hierarchy of Kadomtsev-Petviashvili equation
full work available at URL: https://doi.org/10.1007/bf00419926
OpenAlex ID: W2014390173
description: scientific article; zbMATH DE number 3936028