{"paper":{"title":"On scattering for the defocusing quintic nonlinear Schr\\\"odinger equation on the two-dimensional cylinder","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Xing Cheng, Zehua Zhao, Zihua Guo","submitted_at":"2018-09-05T14:07:56Z","abstract_excerpt":"In this article, we prove the scattering for the quintic defocusing nonlinear Schr\\\"odinger equation on cylinder $\\mathbb{R} \\times \\mathbb{T}$ in $H^1$. We establish an abstract linear profile decomposition in $L^2_x h^\\alpha$, $0 < \\alpha \\le 1$, motivated by the linear profile decomposition of the mass-critical Schr\\\"odinger equation in $L^2(\\mathbb{R}^d )$, $d\\ge 1$. Then by using the solution of the one-discrete-component quintic resonant nonlinear Schr\\\"odinger system, whose scattering can be proved by using the techniques in $1d$ mass critical NLS problem by B. Dodson, to approximate th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.01527","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"}