# On the symplectic phase space of KdV

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.

## 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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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English 2008 14 Jan 2009 16:04 04 Jan 2018 08:02 American Mathematical Society 0002-9939 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. https://doi.org/10.1090/S0002-9939-07-09120-4 http://arxiv.org/abs/0710.1381

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