{"paper":{"title":"Threshold solutions for the focusing $L^{2}$ -supercritical NLS Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Qing Guo","submitted_at":"2011-11-24T02:26:59Z","abstract_excerpt":"We investigate the $L^2$-supercritical and $\\dot{H}^1$-subcritical nonlinear Schr\\\"{o}dinger equation in $H^1$. In \\cite{G1} and \\cite{yuan}, the mass-energy quantity $M(Q)^{\\frac{1-s_{c}}{s_{c}}}E(Q)$ has been shown to be a threshold for the dynamical behavior of solutions of the equation. In the present paper, we study the dynamics at the critical level $M(u)^{\\frac{1-s_{c}}{s_{c}}}E(u)=M(Q)^{\\frac{1-s_{c}}{s_{c}}}E(Q)$ and classify the corresponding solutions using modulation theory, non-trivially generalize the results obtained in \\cite{holmer3} for the 3D cubic Schr\\\"{o}dinger equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.5669","kind":"arxiv","version":1},"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"}