{"paper":{"title":"Decay and scattering of solutions to nonlinear Schr\\\"odinger equations with regular potentials for nonlinearities of sharp growth","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Lifeng Zhao, Ze Li","submitted_at":"2015-02-08T06:03:08Z","abstract_excerpt":"In this paper, we prove the decay and scattering in the energy space for nonlinear Schr\\\"odinger equations with regular potentials in $\\Bbb R^d$ namely, $i{\\partial _t}u + \\Delta u - V(x)u + \\lambda |u|^{p - 1}u = 0$. We will prove decay estimate and scattering of the solution in the small data case when $1+\\frac{2}{d}<p\\le1+\\frac{4}{d-2}$, $d\\ge3$. The index $1+\\frac{2}{d}$ is sharp for scattering concerning the result of W. Strauss [21]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02212","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"}