{"paper":{"title":"Tri-Hamiltonian structure of an asymmetric generalized Ablowitz-Ladik hierarchy and a Frobenius manifold","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.DG","math.MP"],"primary_cat":"nlin.SI","authors_text":"Hanxue Zhang, Qiulan Zhao, Xinyue Li","submitted_at":"2026-06-24T13:58:26Z","abstract_excerpt":"We construct a local tri-Hamiltonian structure of the asymmetric (3,1)-type generalized Ablowitz-Ladik (gAL) hierarchy at the full-dispersive level and rigorously prove its validity using the supervariable technique. All central invariants of the corresponding bi-Hamiltonian structures are computed. In addition, we construct a Frobenius manifold M arising from the dispersionless limit of this hierarchy and show that the dispersionless limits of the first flows of the (3,1)-type gAL hierarchy belong to the Principal Hierarchy of M."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.25846","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.25846/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}