{"paper":{"title":"Elliptic solutions of Boussinesq type lattice equations and the elliptic Nth root of unity","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Da-jun Zhang, Frank W Nijhoff, Ying-ying Sun","submitted_at":"2019-09-06T14:57:25Z","abstract_excerpt":"We establish an infinite family of solutions in terms of elliptic functions of the lattice Boussinesq systems by setting up a direct linearisation scheme, which provides the solution structure for those equations in the elliptic case. The latter, which contains as main structural element a Cauchy kernel on the torus, is obtained from a dimensional reduction of the elliptic direct linearisation scheme of the lattice Kadomtsev-Petviashvili equation, which requires the introduction of a novel technical concept, namely the \"elliptic cube root of unity\". Thus, in order to implement the reduction we"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1909.02948","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/1909.02948/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"}