{"paper":{"title":"KP solitons and total positivity for the Grassmannian","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.AG","math.MP","nlin.SI"],"primary_cat":"math.CO","authors_text":"Lauren Williams, Yuji Kodama","submitted_at":"2011-05-31T20:42:19Z","abstract_excerpt":"Soliton solutions of the KP equation have been studied since 1970, when Kadomtsev and Petviashvili proposed a two-dimensional dispersive wave equation now known as the KP equation. It is well-known that one can use the Wronskian method to construct a soliton solution to the KP equation from each point of the real Grassmannian Gr_kn. More recently several authors have studied the regular solutions that one obtains in this way: these come from points of the totally non-negative part of the Grassmannian (Gr_kn)_{>= 0}. In this paper we exhibit a surprising connection between the theory of total p"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1106.0023","kind":"arxiv","version":3},"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"}