{"paper":{"title":"Strong instability of standing waves for nonlinear Schr\\\"odinger equations with harmonic potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Masahito Ohta","submitted_at":"2016-04-23T21:35:00Z","abstract_excerpt":"We study strong instability of standing waves $e^{i\\omega t} \\phi_{\\omega}(x)$ for nonlinear Schr\\\"odinger equations with $L^2$-supercritical nonlinearity and a harmonic potential, where $\\phi_{\\omega}$ is a ground state of the corresponding stationary problem. We prove that $e^{i\\omega t} \\phi_{\\omega}(x)$ is strongly unstable if $\\partial_{\\lambda}^2 E(\\phi_{\\omega}^{\\lambda}) |_{\\lambda=1}\\le 0$, where $E$ is the energy and $v^{\\lambda}(x)=\\lambda^{N/2} v(\\lambda x)$ is the $L^2$-invariant scaling."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1604.06957","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"}