{"paper":{"title":"Orbital stability of standing waves for a system of nonlinear Schr\\\"{o}dinger equations with three wave interaction","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Alex H. Ardila","submitted_at":"2017-09-28T02:51:42Z","abstract_excerpt":"We study the existence and stability of standing waves solutions of a three-coupled nonlinear Schr\\\"{o}dinger system related to the Raman amplification in a plasma. By means of the concentration-compacteness method, we provide a characterization of the standing waves solutions as minimizers of an energy functional subject to three independent $L^{2}$ mass constraints. As a consequence, we establish existence and orbital stability of solitary waves."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09788","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"}