{"paper":{"title":"Quasi-periodic Solutions of a Derivative Nonlinear Schr\\\"odinger Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Jie Liu","submitted_at":"2014-07-03T13:11:16Z","abstract_excerpt":"This paper is concerned with a one dimensional (1D) derivative nonlinear Schr\\\"odinger equation with periodic boundary conditions \\begin{equation*}\n  \\mi u_t+u_{xx}+\\mi |u|^2u_x=0, \\ \\ x\\in \\mathbb{T}:=\\mathbb{R}/2\\pi\\mathbb{Z}. \\end{equation*} We show that above equation admits a family of real analytic quasi-periodic solutions with two Diophantine frequencies. The proof is based on a partial Birkhoff normal form and KAM method."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.0910","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"}