{"paper":{"title":"Effective integrable dynamics for some nonlinear wave equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Patrick Gerard (LM-Orsay), Sandrine Grellier (MAPMO)","submitted_at":"2011-10-26T07:20:40Z","abstract_excerpt":"We consider the following degenerate half wave equation on the one dimensional torus $$\\quad i\\partial_t u-|D|u=|u|^2u, \\; u(0,\\cdot)=u_0. $$ We show that, on a large time interval, the solution may be approximated by the solution of a completely integrable system-- the cubic Szeg\\\"o equation. As a consequence, we prove an instability result for large $H^s$ norms of solutions of this wave equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5719","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"}