On the symplectic phase space of KdV

Kappeler, T.; Serier, F.; Topalov, P.

doi:10.1090/S0002-9939-07-09120-4

On the symplectic phase space of KdV
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by T. Kappeler, F. Serier and P. Topalov PDF

Proc. Amer. Math. Soc. 136 (2008), 1691-1698 Request permission

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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