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On action-angle variables for the second Poisson bracket of KdV


Kappeler, T; Makarov, M (2000). On action-angle variables for the second Poisson bracket of KdV. Communications in Mathematical Physics, 214(3):651-677.

Abstract

We prove that on the Sobolev spaces Hᴺ (S ¹) (N≥ 0), each leaf of the foliation, induced by the second Poisson bracket of KdV, admits global action-angle variables. The actions with respect to the first bracket raise to the actions with respect to the second bracket. The angles for the first bracket are, at the same time, angles for the second bracket.

Abstract

We prove that on the Sobolev spaces Hᴺ (S ¹) (N≥ 0), each leaf of the foliation, induced by the second Poisson bracket of KdV, admits global action-angle variables. The actions with respect to the first bracket raise to the actions with respect to the second bracket. The angles for the first bracket are, at the same time, angles for the second bracket.

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4 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2000
Deposited On:29 Nov 2010 16:27
Last Modified:05 Apr 2016 13:26
Publisher:Springer
ISSN:0010-3616
Publisher DOI:https://doi.org/10.1007/s002200000282
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1800865
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1003.37038

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