{"paper":{"title":"Rigorous numerics for NLS: bound states, spectra, and controllability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.DS","authors_text":"Holger Teismann, Roberto Castelli","submitted_at":"2013-10-24T09:01:50Z","abstract_excerpt":"In this paper it is demonstrated how rigorous numerics may be applied to the one-dimensional nonlinear Schr\\\"odinger equation (NLS); specifically, to determining bound--state solutions and establishing certain spectral properties of the linearization. Since the results are rigorous, they can be used to complete a recent analytical proof [6] of the local exact controllability of NLS."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6531","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"}