{"paper":{"title":"Ginzburg-Landau equation for dynamical four-wave mixing in gain nonlinear media with relaxation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.PS","authors_text":"France), Kiev), Robert Conte (ENS Cachan et CEA-DAM, Svitlana Bugaychuk (Institute of physics","submitted_at":"2009-11-11T13:07:39Z","abstract_excerpt":"We consider the dynamical degenerate four-wave mixing (FWM) model in a cubic nonlinear medium including both the time relaxation of the induced nonlinearity and the nonlocal coupling. The initial ten-dimensional FWM system can be rewritten as a three-variable intrinsic system (namely the intensity pattern, the amplitude of the nonlinearity and the total net gain) which is very close to the pumped Maxwell-Bloch system. In the case of a purely nonlocal response the initial system reduces to a real damped sine-Gordon (SG) equation. We obtain a new solution of this equation in the form of a sech f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.2129","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"}