{"paper":{"title":"An hbar-expansion of the Toda hierarchy: a recursive construction of solutions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.MP","math.QA","nlin.SI"],"primary_cat":"math-ph","authors_text":"Kanehisa Takasaki, Takashi Takebe","submitted_at":"2011-12-02T22:58:29Z","abstract_excerpt":"A construction of general solutions of the \\hbar-dependent Toda hierarchy is presented. The construction is based on a Riemann-Hilbert problem for the pairs (L,M) and (\\bar L,\\bar M) of Lax and Orlov-Schulman operators. This Riemann-Hilbert problem is translated to the language of the dressing operators W and \\bar W. The dressing operators are set in an exponential form as W = e^{X/\\hbar} and \\bar W = e^{\\phi/\\hbar}e^{\\bar X/\\hbar}, and the auxiliary operators X,\\bar X and the function \\phi are assumed to have \\hbar-expansions X = X_0 + \\hbar X_1 + ..., \\bar X = \\bar X_0 + \\hbar\\bar X_1 + ... "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0601","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"}