# 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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