{"paper":{"title":"Invariant Cantor manifolds of quasi-periodic solutions for the derivative nonlinear Schrodinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jianjun Liu, Meina Gao","submitted_at":"2018-05-07T02:32:37Z","abstract_excerpt":"This paper is concerned with the derivative nonlinear Schrodinger equation with periodic boundary conditions\n  $$\\mathbf{i}u_t+u_{xx}+\\mathbf{i}\\Big(f(x,u,\\bar{u})\\Big)_x=0,\\quad x\\in\\mathbb{T}:=\\mathbb{R}/2\\pi\\mathbb{Z},$$ where $f$ is an analytic function of the form $$f(x,u,\\bar{u})=\\mu|u|^2u+f_{\\geq4}(x,u,\\bar{u}),\\quad 0\\neq\\mu\\in\\mathbb{R},$$ and $f_{\\geq4}(x,u,\\bar{u})$ denotes terms of order at least four in $u,\\bar{u}$. We show the above equation possesses Cantor families of smooth quasi-periodic solutions of small amplitude. The proof is based on an infinite dimensional KAM theorem f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.02321","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"}