{"paper":{"title":"Matrix KP: tropical limit, Yang-Baxter and pentagon maps","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"nlin.SI","authors_text":"Aristophanes Dimakis, Folkert M\\\"uller-Hoissen","submitted_at":"2017-09-28T08:42:43Z","abstract_excerpt":"In the tropical limit of matrix KP-II solitons, their support at fixed time is a planar graph with \"polarizations\" attached to its linear parts. In this work we explore a subclass of soliton solutions whose tropical limit graph has the form of a rooted and generically binary tree, as well as solutions with a limit graph consisting of two relatively inverted such rooted tree graphs. The distribution of polarizations over the constituting lines of the graph is fully determined by a parameter-dependent binary operation and a (in general non-linear) Yang-Baxter map, which in the vector KP case bec"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.09848","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"}