{"paper":{"title":"Equipartition of Mass in Nonlinear Schr\\\"odinger / Gross-Pitaevskii Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.PS"],"primary_cat":"math.AP","authors_text":"Michael I. Weinstein, Zhou Gang","submitted_at":"2010-11-09T20:28:48Z","abstract_excerpt":"We study the infinite time dynamics of a class of nonlinear Schr\\\"odinger / Gross-Pitaevskii equations. In our previous paper, we prove the asymptotic stability of the nonlinear ground state in a general situation which admits degenerate neutral modes of arbitrary finite multiplicity, a typical situation in systems with symmetry. Neutral modes correspond to purely imaginary (neutrally stable) point spectrum of the linearization of the Hamiltonian PDE about a critical point. In particular, a small perturbation of the nonlinear ground state, which typically excites such neutral modes and radiati"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.2192","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"}