{"paper":{"title":"Instability of Standing Waves to the Inhomogeneous Nonlinear Schr\\\"odinger Equation with Harmonic Potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jianqing Chen, Yue Liu","submitted_at":"2008-09-11T16:05:47Z","abstract_excerpt":"We study the instability of standing-wave solutions $e^{i\\omega t}\\phi_{\\omega}(x)$ to the inhomogeneous nonlinear Schr\\\"{o}dinger equation $$i\\phi_t=-\\triangle\\phi+|x|^2\\phi-|x|^b|\\phi|^{p-1}\\phi, \\qquad \\in\\mathbb{R}^N, $$ where $ b > 0 $ and $ \\phi_{\\omega} $ is a ground-state solution. The results of the instability of standing-wave solutions reveal a balance between the frequency $\\omega $ of wave and the power of nonlinearity $p $ for any fixed $ b > 0. $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0809.2035","kind":"arxiv","version":5},"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"}