{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T05:08:54Z","timestamp":1775538534294,"version":"3.50.1"},"reference-count":31,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2022,3,7]],"date-time":"2022-03-07T00:00:00Z","timestamp":1646611200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["12071432"],"award-info":[{"award-number":["12071432"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11401529"],"award-info":[{"award-number":["11401529"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LY18A010033"],"award-info":[{"award-number":["LY18A010033"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Natural Science Foundation of Zhejiang Province","doi-asserted-by":"publisher","award":["LY17A010024"],"award-info":[{"award-number":["LY17A010024"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we seek connections between the Sylvester equation and Kadomtsev\u2013Petviashvili system. By introducing Sylvester equation LM are bold, please chekc if bold neceaasry, if not, please remove all bold of equation \u2212MK = rsT together with an evolution equation set of r and s, master function S(i,j)=sTKjC(I + MC)\u22121Lir is used to construct the Kadomtsev\u2013Petviashvili system, including the Kadomtsev\u2013Petviashvili equation, modified Kadomtsev\u2013Petviashvili equation and Schwarzian Kadomtsev\u2013Petviashvili equation. The matrix M provides \u03c4-function by \u03c4 = |I + MC|. With the help of some recurrence relations, the reductions to the Korteweg\u2013de Vries and Boussinesq systems are discussed.<\/jats:p>","DOI":"10.3390\/sym14030542","type":"journal-article","created":{"date-parts":[[2022,3,9]],"date-time":"2022-03-09T01:50:53Z","timestamp":1646790653000},"page":"542","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":11,"title":["The Sylvester Equation and Kadomtsev\u2013Petviashvili System"],"prefix":"10.3390","volume":"14","author":[{"given":"Wei","family":"Feng","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3726-1365","authenticated-orcid":false,"given":"Songlin","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,7]]},"reference":[{"key":"ref_1","first-page":"115","article-title":"Sur l\u2019equation en matrices px=xq","volume":"99","author":"Sylvester","year":"1884","journal-title":"C. 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