{"paper":{"title":"Periodic Orbits of Gross Pitaevskii in the Disc with Vortices Following Point Vortex Flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.DS"],"primary_cat":"math.AP","authors_text":"Raghavendra Venkatraman","submitted_at":"2016-02-29T16:55:28Z","abstract_excerpt":"We prove the existence of non-constant time periodic vortex solutions to the Gross-Pitaevskii equations for small but \\textit{fixed} $\\varepsilon > 0.$ The vortices of these solutions follow periodic orbits to the point vortex system of ordinary differential equations \\textit{for all time}. The construction uses two approaches-- constrained minimization techniques adapted from \\cite{GS} and topological minimax techniques adapted from \\cite{LinMinMax}, applied to a formulation of the problem within a rotational ansatz."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.09040","kind":"arxiv","version":3},"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"}