{"paper":{"title":"On long time dynamics of perturbed KdV equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Guan Huang","submitted_at":"2013-10-21T08:46:27Z","abstract_excerpt":"Consider perturbed KdV equations: \\[u_t+u_{xxx}-6uu_x=\\epsilon f(u(\\cdot)),\\quad x\\in\\mathbb{T}=\\mathbb{R}/\\mathbb{Z},\\;\\int_{\\mathbb{T}}u(x,t)dx=0,\\] where the nonlinearity defines analytic operators $u(\\cdot)\\mapsto f(u(\\cdot))$ in sufficiently smooth Sobolev spaces. Assume that the equation has an $\\epsilon$-quasi-invariant measure $\\mu$ and satisfies some additional mild assumptions. Let $u^{\\epsilon}(t)$ be a solution. Then on time intervals of order $\\epsilon^{-1}$, as $\\epsilon\\to0$, its actions $I(u^{\\epsilon}(t,\\cdot))$ can be approximated by solutions of a certain well-posed averaged"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.5462","kind":"arxiv","version":2},"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"}