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La structure symplectique de l'espace de phase de l'équation Korteweg-de Vries périodique


Bättig, D; Bloch, A; Guillot, J C; Kappeler, T (1993). La structure symplectique de l'espace de phase de l'équation Korteweg-de Vries périodique. Comptes Rendus de l'Académie des Sciences. Série I. Mathématique, 317(11):1019-1022.

Abstract

e prove that the generalized phase space of the Korteweg-de Vries equation on S1, i.e., (L20([0,1]),ωG), where ωG is the Gardner symplectic structure on the space L20([0,1]) of L2 functions with mean zero, is symplectomorphic to the phase space (l21/2(R2),ω0) of infinitely many harmonic oscillators, where l21/2(R2) is the Hilbert space of sequences (xn,yn)n≥1 satisfying ∑n≥1n(x2n+y2n)<∞ endowed with the canonical symplectic structure ω0. The symplectomorphism Ω from (L20([0,1]),ωG) onto (l21/2(R2),ω0) is shown to be bianalytic. Similar results hold for the periodic Toda equations and the periodic nonlinear Schrödinger equation.

Abstract

e prove that the generalized phase space of the Korteweg-de Vries equation on S1, i.e., (L20([0,1]),ωG), where ωG is the Gardner symplectic structure on the space L20([0,1]) of L2 functions with mean zero, is symplectomorphic to the phase space (l21/2(R2),ω0) of infinitely many harmonic oscillators, where l21/2(R2) is the Hilbert space of sequences (xn,yn)n≥1 satisfying ∑n≥1n(x2n+y2n)<∞ endowed with the canonical symplectic structure ω0. The symplectomorphism Ω from (L20([0,1]),ωG) onto (l21/2(R2),ω0) is shown to be bianalytic. Similar results hold for the periodic Toda equations and the periodic nonlinear Schrödinger equation.

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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:French
Date:1993
Deposited On:18 Feb 2010 12:14
Last Modified:05 Apr 2016 13:28
Publisher:Elsevier
ISSN:0151-0509
Related URLs:http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0816.35119

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