{"paper":{"title":"The Rogue Wave and breather solution of the Gerdjikov-Ivanov equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Jingsong He, Shuwei Xu","submitted_at":"2011-09-15T08:01:06Z","abstract_excerpt":"The Gerdjikov-Ivanov (GI) system of $q$ and $r$ is defined by a quadratic polynomial spectral problem with $2 \\times 2$ matrix coefficients. Each element of the matrix of n-fold Darboux transformation of this system is expressed by a ratio of $(n+1)\\times (n+1)$ determinant and $n\\times n$ determinant of eigenfunctions, which implies the determinant representation of $q^{[n]}$ and $r^{[n]}$ generated from known solution $q$ and $r$. By choosing some special eigenvalues and eigenfunctions according to the reduction conditions $q^{[n]}=-(r^{[n]})^*$, the determinant representation of $q^{[n]}$ p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.3283","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"}