{"paper":{"title":"Variational properties and orbital stability of standing waves for NLS equation on a star graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"C. Cacciapuoti, D. Finco, D. Noja, R. Adami","submitted_at":"2012-06-22T16:49:07Z","abstract_excerpt":"We study standing waves for a nonlinear Schr\\\"odinger equation on a star graph {$\\mathcal{G}$} i.e. $N$ half-lines joined at a vertex. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\\alpha\\leqslant 0$. The nonlinearity is of focusing power type. The dynamics is given by an equation of the form $ i \\frac{d}{dt}\\Psi_t = H \\Psi_t - | \\Psi_t |^{2\\mu} \\Psi_t $, where $H$ is the Hamiltonian operator which generates the linear Schr\\\"odinger dynamics. We show the existence of several families of standing waves for every sign of the coupling at the ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.5201","kind":"arxiv","version":3},"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"}