{"paper":{"title":"Nonlinear fractional Schr\\\"odinger equations in one dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alexandru D. Ionescu, Fabio Pusateri","submitted_at":"2012-09-22T00:16:26Z","abstract_excerpt":"We consider the question of global existence of small, smooth, and localized solutions of a certain fractional semilinear cubic NLS in one dimension, $$i\\partial_t u - \\Lambda u = c_0{|u|}^2 u + c_1 u^3 + c_2 u \\bar{u}^2 + c_3 \\bar{u}^3, \\qquad \\Lambda = \\Lambda(\\partial_x) = {|\\partial_x|}^(1/2)$$, where $c_0\\in\\mathbb{R}$ and $c_1,c_2,c_3\\in\\mathbb{C}$. This model is motivated by the two-dimensional water waves equations, which have a somewhat similar structure in the Eulerian formulation, in the case of irrotational flows. We show that one cannot expect linear scattering, even in this simpl"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1209.4943","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"}