{"paper":{"title":"Asymptotic stability for standing waves of a NLS equation with concentrated nonlinearity in dimension three. II","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Cecilia Ortoleva, Diego Noja, Riccardo Adami","submitted_at":"2015-07-16T15:56:35Z","abstract_excerpt":"We investigate the asymptotic stability of standing waves for a model of Schr\\\"odinger equation with spatially concentrated nonlinearity in space dimension three. The nonlinearity studied is a power nonlinearity concentrated at the point $x=0$ obtained considering a contact (or $\\delta$) interaction with strength $\\alpha$, and letting the strength $\\alpha$ depend on the wavefunction in a prescribed way. For power nonlinearities in the range $(\\frac{1}{\\sqrt 2},1)$ there exist orbitally stable standing waves $\\Phi_\\omega$, and the linearization around them admits two imaginary eigenvalues which"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.04626","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"}