{"paper":{"title":"On the standing waves of the NLS-log equation with point interaction on a star graph","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"Nataliia Goloshchapova","submitted_at":"2018-03-19T23:24:36Z","abstract_excerpt":"We study a nonlinear Schr\\\"odinger equation with logarithmic nonlinearity on a star graph $\\mathcal{G}$. At the vertex an interaction occurs described by a boundary condition of delta type with strength $\\alpha\\in \\mathbb{R}$. We investigate orbital stability and spectral instability of the standing wave solutions $e^{i\\omega t}\\mathbf{\\Phi}(x)$ to the equation when the profile $\\mathbf\\Phi(x)$ has mixed structure (i.e. has bumps and tails). In our approach we essentially use the extension theory of symmetric operators by Krein - von Neumann, and the analytic perturbations theory."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.07194","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"}