{"paper":{"title":"Final state problem for the cubic nonlinear Schr\"odinger equation with repulsive delta potential","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jun-ichi Segata","submitted_at":"2014-02-21T01:57:10Z","abstract_excerpt":"We consider the asymptotic behavior in time of solutions to the cubic nonlinear Schr\"odinger equation with repulsive delta potential (delta-NLS). We shall prove that for a given asymptotic profile, there exists a solution to (delta-NLS) which converges to the given asymptotic profile as time goes infinity. To show this result we exploit the distorted Fourier transform associated to the Schr\"odinger equation with delta potential."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.5185","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"}