{"paper":{"title":"Kadomtsev-Petviashvili system and reduction: generalized Cauchy matrix approach","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"nlin.SI","authors_text":"Shou-Feng Shen, Song-lin Zhao, Wei Feng","submitted_at":"2014-04-11T09:19:18Z","abstract_excerpt":"By the Sylvester equation $\\bL\\bM-\\bM\\bK=\\br\\bs^{\\st}$ together with an evolution equation set of $\\br$ and $\\bs$, generalized Cauchy matrix approach is established to investigate exact solutions for Kadomtsev-Petviashvili system, including Kadomtsev-Petviashvili equation, modified Kadomtsev-Petviashvili equation and Schwarzian Kadomtsev-Petviashvili equation. The matrix $\\bM$ provides $\\tau$-function by $\\tau=|\\bI+\\bM\\bC|$. With the help of some recurrence relations, the reduction to Korteweg-de Vries system, Boussinesq system and extended Boussinesq system are also discussed."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3043","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"}