{"paper":{"title":"Rogue waves of the Hirota and the Maxwell-Bloch equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Chuanzhong Li, Jingsong He, K. Porsezian","submitted_at":"2012-05-06T08:17:14Z","abstract_excerpt":"In this paper, we derive a Darboux transformation of the Hirota and the Maxwell-Bloch(H-MB) system which is governed by femtosecond pulse propagation through an erbium doped fibre and further generalize it to the matrix form of the $n$-fold Darboux transformation of this system. This $n$-fold Darboux transformation implies the determinant representation of $n$-th new solutions of $(E^{[n]},p^{[n]}, \\eta^{[n]})$ generated from known solution of $(E, p,\\eta)$. The determinant representation of $(E^{[n]},p^{[n]} ,\\eta^{[n]})$ provides soliton solutions, positon solutions, and breather solutions ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.1191","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"}