{"paper":{"title":"On the existence of full dimensional KAM torus for nonlinear Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Hongzi Cong, Lufang Mi, Yuan Wu, Yunfeng Shi","submitted_at":"2019-03-01T02:18:16Z","abstract_excerpt":"In this paper, we study the following nonlinear Schr\\\"odinger equation \\begin{eqnarray}\\label{maineq0} \\textbf{i}u_{t}-u_{xx}+V*u+\\epsilon f(x)|u|^4u=0,\\ x\\in\\mathbb{T}=\\mathbb{R}/2\\pi\\mathbb{Z}, \\end{eqnarray} where $V*$ is the Fourier multiplier defined by $\\widehat{(V* u})_n=V_{n}\\widehat{u}_n, V_n\\in[-1,1]$ and $f(x)$ is Gevrey smooth. It is shown that for $0\\leq|\\epsilon|\\ll1$, there is some $(V_n)_{n\\in\\mathbb{Z}}$ such that, the equation admits a time almost periodic solution (i.e., full dimensional KAM torus) in the Gevrey space. This extends results of Bourgain \\cite{BJFA2005} and Con"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.00127","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"}