{"paper":{"title":"The point-like limit for a NLS equation with concentrated nonlinearity in dimension three","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Alessandro Teta, Claudio Cacciapuoti, Diego Noja, Domenico Finco","submitted_at":"2015-11-20T19:24:48Z","abstract_excerpt":"We consider a scaling limit of a nonlinear Schr\\\"odinger equation (NLS) with a nonlocal nonlinearity showing that it reproduces in the limit of cutoff removal a NLS equation with nonlinearity concentrated at a point. The regularized dynamics is described by the equation \\begin{equation*} i\\frac{\\partial }{\\partial t} \\psi^\\varepsilon(t)= -\\Delta \\psi^\\varepsilon(t) + g(\\varepsilon,\\mu,|(\\rho^\\varepsilon,\\psi^\\varepsilon(t))|^{2\\mu}) (\\rho^\\varepsilon,\\psi^\\varepsilon(t)) \\rho^\\varepsilon \\end{equation*} where $\\rho^{\\varepsilon} \\to \\delta_0$ weakly and the function $g$ embodies the nonlineari"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06731","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"}