{"paper":{"title":"On the Dynamics of solitons in the nonlinear Schroedinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.MP"],"primary_cat":"math-ph","authors_text":"Anna Maria Micheletti, Marco Ghimenti, Vieri Benci","submitted_at":"2011-04-20T10:48:55Z","abstract_excerpt":"We study the behavior of the soliton solutions of the equation i((\\partial{\\psi})/(\\partialt))=-(1/(2m)){\\Delta}{\\psi}+(1/2)W_{{\\epsilon}}'({\\psi})+V(x){\\psi} where W_{{\\epsilon}}' is a suitable nonlinear term which is singular for {\\epsilon}=0. We use the \"strong\" nonlinearity to obtain results on existence, shape, stability and dynamics of the soliton. The main result of this paper (Theorem 1) shows that for {\\epsilon}\\to0 the orbit of our soliton approaches the orbit of a classical particle in a potential V(x)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.3989","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"}