{"paper":{"title":"Localizing Estimates of the Support of Solutions of some Nonlinear Schr\\\"{o}dinger Equations - The Stationary Case","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jes\\'us Ildefonso D\\'iaz, Pascal B\\'egout","submitted_at":"2010-12-08T10:30:23Z","abstract_excerpt":"The main goal of this paper is to study the nature of the support of the solution of suitable nonlinear Schr\\\"{o}dinger equations mainly the compactness of the support and its spatial localization. This question is very related with pure essence of the derivation of the Schr\\\"{o}dinger equation since it is well-known that if the linear Schr\\\"{o}dinger equation is perturbated with \"regular\" potentials then the corresponding solution never vanishes on a positive measured subset of the domain, which corresponds with the impossibility of localize the particle. Here we shall prove that if the pertu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1012.1729","kind":"arxiv","version":3},"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"}