On the convexity of the KdV Hamiltonian
| Autor: | Kappeler, Thomas, Maspero, Alberto, Molnar, Jan-Cornelius, Topalov, Peter |
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| Rok vydání: | 2015 |
| Předmět: | |
| Zdroj: | Communications in Mathematical Physics, 346(1): 191-236, 2016 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s00220-015-2563-x |
| Popis: | 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 $\ell_{\mathbb C}^{2}(\mathbb N)$. Comment: 48 pages |
| Databáze: | arXiv |
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