{"paper":{"title":"Toda Hierarchy with Indefinite Metric","license":"","headline":"","cross_cats":["hep-th","nlin.SI"],"primary_cat":"solv-int","authors_text":"Jian Ye, Yuji Kodama","submitted_at":"1995-05-19T15:17:21Z","abstract_excerpt":"We consider a generalization of the full symmetric Toda hierarchy where the matrix $\\tilde {L}$ of the Lax pair is given by $\\tilde {L}=LS$, with a full symmetric matrix $L$ and a nondegenerate diagonal matrix $S$. The key feature of the hierarchy is that the inverse scattering data includes a class of noncompact groups of matrices, such as $O(p,q)$. We give an explicit formula for the solution to the initial value problem of this hierarchy. The formula is obtained by generalizing the orthogonalization procedure of Szeg\\\"{o}, or the QR factorization method of Symes. The behaviors of the soluti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"solv-int/9505004","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"}