{"paper":{"title":"Linear integral equations and two-dimensional Toda systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Wei Fu, Yue Yin","submitted_at":"2021-04-13T11:55:14Z","abstract_excerpt":"The direct linearisation framework is presented for the two-dimensional Toda equations associated with the infinite-dimensional Lie algebras $A_\\infty$, $B_\\infty$ and $C_\\infty$, as well as the Kac--Moody algebras $A_{r}^{(1)}$, $A_{2r}^{(2)}$, $C_{r}^{(1)}$ and $D_{r+1}^{(2)}$ for arbitrary integers $r\\in\\mathbb{Z}^+$, from the aspect of a set of linear integral equations in a certain form. Such a scheme not only provides a unified perspective to understand the underlying integrability structure, but also induces the direct linearising type solution potentially leading to the universal solut"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2104.06123","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2104.06123/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"}