{"paper":{"title":"Instability of bound states of a nonlinear Schr\\\"odinger equation with a Dirac potential","license":"","headline":"","cross_cats":["nlin.SI"],"primary_cat":"nlin.PS","authors_text":"Baruch Ksherim, Gadi Fibich, Reika Fukuizumi, Stefan Le-Coz, Yonatan Sivan","submitted_at":"2007-07-17T12:26:23Z","abstract_excerpt":"We study analytically and numerically the stability of the standing waves for a nonlinear Schr\\\"odinger equation with a point defect and a power type nonlinearity. A main difficulty is to compute the number of negative eigenvalues of the linearized operator around the standing waves, and it is overcome by a perturbation method and continuation arguments. Among others, in the case of a repulsive defect, we show that the standing wave solution is stable in $\\hurad$ and unstable in $\\hu$ under subcritical nonlinearity. Further we investigate the nature of instability: under critical or supercriti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0707.2491","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"}