{"paper":{"title":"On scattering for the cubic defocusing nonlinear Schr\\\"odinger equation on waveguide $\\mathbb{R}^2\\times \\mathbb{T}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Kailong Yang, Lifeng Zhao, Xing Cheng, Zihua Guo","submitted_at":"2017-05-02T13:21:30Z","abstract_excerpt":"In this article, we will show the global wellposedness and scattering of the cubic defocusing nonlinear Schr\\\"odinger equation on waveguide $\\mathbb{R}^2\\times \\mathbb{T}$ in $H^1$. We first establish the linear profile decomposition in $H^{ 1}(\\mathbb{R}^2 \\times \\mathbb{T})$ motivated by the linear profile decomposition of the mass-critical Schr\\\"odinger equation in $L^2(\\mathbb{R}^2)$. Then by using the solution of the infinite dimensional vector-valued resonant nonlinear Schr\\\"odinger system to approximate the nonlinear profile, we can prove scattering in $H^1$ by using the concentration-c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.00954","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"}