We prove that the Birkhoff map $ \Omega$ for KdV constructed on $ H^{-1}_0(\mathbb{T})$ can be interpolated between $ H^{-1}_0(\mathbb{T})$ and $ L^2_0(\mathbb{T})$. In particular, the symplectic phase space $ H^{1/2}_0(\mathbb{T})$ can be described in terms of Birkhoff coordinates.

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Kappeler, T; Serier, F; Topalov, P (2008). *On the symplectic phase space of KdV.* Proceedings of the American Mathematical Society, 136(5):1691-1698.

## Abstract

We prove that the Birkhoff map $ \Omega$ for KdV constructed on $ H^{-1}_0(\mathbb{T})$ can be interpolated between $ H^{-1}_0(\mathbb{T})$ and $ L^2_0(\mathbb{T})$. In particular, the symplectic phase space $ H^{1/2}_0(\mathbb{T})$ can be described in terms of Birkhoff coordinates.

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 2008 |

Deposited On: | 14 Jan 2009 16:04 |

Last Modified: | 05 Apr 2016 12:39 |

Publisher: | American Mathematical Society |

ISSN: | 0002-9939 |

Additional Information: | First published in Kappeler, T; Serier, F; Topalov, P (2008). On the symplectic phase space of KdV. Proceedings of the American Mathematical Society, 136(5):1691-1698, published by the American Mathematical Society. |

Publisher DOI: | 10.1090/S0002-9939-07-09120-4 |

Related URLs: | http://arxiv.org/abs/0710.1381 |

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