{"paper":{"title":"Asymptotic behavior of the Schr\\\"odinger-Debye system with refractive index of square wave amplitude","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Adan J. Corcho, Juan C. Cordero","submitted_at":"2017-05-02T14:45:41Z","abstract_excerpt":"We obtain local well-posedness for the one-dimensional Schr\\\"odinger-Debye interactions in nonlinear optics in the spaces $L^2\\times L^p,\\; 1\\le p < \\infty$. When $p=1$ we show that the local solutions extend globally. In the focusing regime, we consider a family of solutions $\\{(u_{\\tau}, v_{\\tau})\\}_{\\tau>0}$ in $ H^1\\times H^1$ associated to an initial data family $\\{(u_{\\tau_0},v_{\\tau_0})\\}_{\\tau>0}$ uniformly bounded in $H^1\\times L^2$, where $\\tau$ is a small response time parameter. We prove prove that $(u_{\\tau}, v_{\\tau})$ converges to $(u, -|u|^2)$ in the space $L^{\\infty}_{[0, T]}L"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.01003","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"}