{"paper":{"title":"On the Periodic Cauchy problem for a coupled system of third-order nonlinear Schr\\\"odinger equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Luciana Bragan\\c{c}a, Marcia Scialom","submitted_at":"2014-11-24T20:21:12Z","abstract_excerpt":"We investigate some well-posedness issues for the initial value problem (IVP) associated to the system \\begin{equation} \\{ \\begin{array} [c]{l} 2i\\partial_{t}u+q\\partial_{x}^{2}u+i\\gamma\\partial_{x}^{3}u=F_{1}(u,w)\\\\ 2i\\partial_{t}w+q\\partial_{x}^{2}w+i\\gamma\\partial_{x}^{3}w=F_{2}(u,w), \\end{array} . \\end{equation} where $F_{1}$ and $F_{2}$ are polynomials of degree 3 involving $u$, $w$ and their derivatives. This system describes the dynamics of two nonlinear short-optical pulses envelopes $u(x,t)$ and $w(x,t)$ in fibers (\\cite{31}, \\cite{14}). We prove periodic local well-posedness for the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.6599","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"}