{"paper":{"title":"Self-similar solutions with compactly supported profile of some nonlinear Schr{\\\"o}dinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jes\\'us Ildefonso D\\'iaz (UCM), Pascal B\\'egout (IMT)","submitted_at":"2013-01-04T13:15:08Z","abstract_excerpt":"This paper deals with the study of \"\\textit{sharp localized}\" solutions of a nonlinear type Schr{\\\"o}dinger equation in the whole space $\\R^N,$ $N\\ge1,$ with a zero order term, in modulus, like a power $m$ less than one of the modulus of the solution, and with a non zero external forcing term $\\f.$ Our fundamental assumption is that such an exponent $m$ verifies $m\\in (0,1).$ The self-similar structure of the solution is justified from the assumption that the external forcing term satisfies that $\\f(t,x)=t^{-(\\vp-2)/2}\\F(t^{-1/2}x)$ for some complex exponent $\\vp$ and for some profile function"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.0715","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"}