{"paper":{"title":"On the convexity of the KdV Hamiltonian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alberto Maspero, Jan-Cornelius Molnar, Peter Topalov, Thomas Kappeler","submitted_at":"2015-02-20T12:45:47Z","abstract_excerpt":"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 $\\ell_{\\mathbb C}^{2}(\\mathbb N)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.05857","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}