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arXiv · 1502.05857

On the convexity of the KdV Hamiltonian

Thomas Kappeler·Alberto Maspero·Jan-Cornelius Molnar·Peter Topalov
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Abstract

We prove that the nonlinear part $H^{*}$ of the KdV Hamiltonian $H^{kdv}$, when expressed in action variables $I = (I_{n})_{n\ge 1}$, extends to a real analytic function on the positive quadrant $\ell^2_+(\mathbb N)$ of $\ell^{2}(\mathbb N)$ and is strictly concave near $0$. As a consequence, the differential of $H^{*}$ defines a local diffeomorphism near $0$ of $\ell_{\mathbb C}^{2}(\mathbb N)$.

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Thomas Kappeler, Alberto Maspero, Jan-Cornelius Molnar, Peter Topalov. 2015-02-20. On the convexity of the KdV Hamiltonian. https://doi.org/10.1007/s00220-015-2563-x

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