{"paper":{"title":"On a quasilinear non-local Benney System","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Filipe Oliveira, Jo\\~ao-Paulo Dias","submitted_at":"2015-12-02T20:41:08Z","abstract_excerpt":"We study the quasilinear non-local Benney System\n  $$\\left\\{\\begin{array}{llll} iu_t+u_{xx}=|u|^2u+buv\\\\ v_t+a(\\int_{\\mathbf{R}^+}v^2dx)v_x=-b(|u|^2)_x,\\quad (x,t)\\in\\mathbf{R}^+\\times [0,T],\\, T>0. \\end{array}\\right.$$\n  We establish the existence and uniqueness of strong local solutions to the corresponding Cauchy problem and show, under certain conditions, the blow-up of such solutions in finite time. Furthermore, we prove the existence of global weak solutions and exhibit bound-state solutions to this system."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00837","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"}