{"paper":{"title":"Existence and stability of standing waves for nonlinear Schrodinger systems involving the fractional Laplacian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.AP","authors_text":"Santosh Bhattarai","submitted_at":"2016-04-06T18:35:00Z","abstract_excerpt":"In the present paper we consider the coupled system of nonlinear Schr\\\"{o}dinger equations with the fractional Laplacian \\[ \\left\\{ \\begin{aligned}\n  (-\\Delta)^\\alpha u_1 & = \\lambda_1u_1+f_1(u_1)+\\partial_1F(u_1,u_2)\\ \\ \\mathrm{in}\\ \\mathbb{R}^N, \\\\\n  (-\\Delta)^\\alpha u_2 & = \\lambda_2u_2+f_2(u_2)+\\partial_2F(u_1,u_2)\\ \\ \\mathrm{in}\\ \\mathbb{R}^N, \\end{aligned} \\right. \\] where $u_1, u_2:\\mathbb{R}^N\\to \\mathbb{C},\\ N\\geq 2,$ and $0<\\alpha<1.$ By studying an appropriate family of constrained minimization problems, we obtain the existence of solutions in the space $H^\\alpha(\\mathbb{R}^N) \\time"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.01718","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"}