{"paper":{"title":"Phase turbulence in the Complex Ginzburg--Landau equation via Kuramoto--Sivashinsky phase dynamics","license":"","headline":"","cross_cats":["math.AP","math.MP","physics.flu-dyn"],"primary_cat":"math-ph","authors_text":"Guillaume van Baalen","submitted_at":"2003-02-10T13:40:52Z","abstract_excerpt":"We study the Complex Ginzburg--Landau initial value problem $\\partial_t u=(1+i\\alpha) \\partial_x^2 u + u - (1+i\\beta) u |u|^2$, $u(x,0)=u_0(x)$ for a complex field $u\\in{\\bf C}$, with $\\alpha,\\beta\\in{\\bf R}$. We consider the Benjamin--Feir linear instability region $1+\\alpha\\beta=-\\epsilon^2$ with $\\epsilon\\ll1$ and $\\alpha^2<1/2$.\n  We show that for all $\\epsilon\\leq{\\cal O}(\\sqrt{1-2\\alpha^2} L_0^{-32/37})$, and for all initial data $u_0$ sufficiently close to 1 (up to a global phase factor $\\ed^{i \\phi_0}, \\phi_0\\in{\\bf R}$) in the appropriate space, there exists a unique (spatially) perio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math-ph/0302021","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"}