# On the convexity of the KdV Hamiltonian

Authors
Type
Preprint
Publication Date
Feb 20, 2015
Submission Date
Feb 20, 2015
Identifiers
arXiv ID: 1502.05857
Source
arXiv
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 $\ell_{\mathbb C}^{2}(\mathbb N)$.