{"paper":{"title":"Exact Poisson pencils, $\\tau$-structures and topological hierarchies","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Gregorio Falqui, Paolo Lorenzoni","submitted_at":"2011-06-08T12:15:48Z","abstract_excerpt":"We discuss, in the framework of Dubrovin-Zhang's perturbative approach to integrable evolutionary PDEs in 1+1 dimensions, the role of a special class of Poisson pencils, called exact Poisson pencils. In particular we show that, in the semisimple case, exactness of the pencil is equivalent to the constancy of the so-called \"central invariants\" of the theory that were introduced by Dubrovin, Liu and Zhang."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.1546","kind":"arxiv","version":2},"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"}