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.

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.

## Citations

## 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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