{"paper":{"title":"The Lugiato-Lefever equation with nonlinear damping caused by two photon absorption","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Janina G\\\"artner, Rainer Mandel, Wolfgang Reichel","submitted_at":"2018-11-29T14:36:46Z","abstract_excerpt":"In this paper we investigate the effect of nonlinear damping on the Lugiato-Lefever equation $$ \\i \\partial_t a = -(\\i-\\zeta) a - da_{xx} -(1+\\i\\kappa)|a|^2a +\\i f $$ on the torus or the real line. For the case of the torus it is shown that for small nonlinear damping $\\kappa>0$ stationary spatially periodic solutions exist on branches that bifurcate from constant solutions whereas all nonconstant solutions disappear when the damping parameter $\\kappa$ exceeds a critical value. These results apply both for normal ($d<0$) and anomalous ($d>0$) dispersion. For the case of the real line we show b"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.12200","kind":"arxiv","version":3},"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"}