{"paper":{"title":"A Nekhoroshev type theorem for the nonlinear Schr\\\"odinger equation on the d-dimensional torus.","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Benoit Grebert (LMJL), Erwan Faou (INRIA - IRMAR)","submitted_at":"2010-03-25T10:31:51Z","abstract_excerpt":"We prove a Nekhoroshev type theorem for the nonlinear Schr\\\"odinger equation $$ iu_t=-\\Delta u+V\\star u+\\partial_{\\bar u}g(u,\\bar u)\\, \\quad x\\in \\T^d, $$ where $V$ is a typical smooth potential and $g$ is analytic in both variables. More precisely we prove that if the initial datum is analytic in a strip of width $\\rho>0$ with a bound on this strip equals to $\\eps$ then, if $\\eps$ is small enough, the solution of the nonlinear Schr\\\"odinger equation above remains analytic in a strip of width $\\rho/2$ and bounded on this strip by $C\\eps$ during very long time of order $ \\eps^{-\\alpha|\\ln \\eps|"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.4845","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"}