{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T14:35:48Z","timestamp":1753886148126,"version":"3.41.2"},"reference-count":19,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,4,5]],"date-time":"2012-04-05T00:00:00Z","timestamp":1333584000000},"content-version":"vor","delay-in-days":95,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>Through assuming that nonlinear superposition principles (NLSPs) are embedded in a Lie group, a class of 3rd\u2010order PDEs is derived from a general determining equation that determine the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the governing PDE is proved <jats:italic>C<\/jats:italic>\u2010integrable. In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation.<\/jats:p>","DOI":"10.1155\/2012\/346824","type":"journal-article","created":{"date-parts":[[2012,4,5]],"date-time":"2012-04-05T21:17:14Z","timestamp":1333660634000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Class of PDEs with Nonlinear Superposition Principles"],"prefix":"10.1155","volume":"2012","author":[{"given":"Li","family":"Peng","sequence":"first","affiliation":[]},{"given":"Liu","family":"Keying","sequence":"additional","affiliation":[]},{"given":"Pan","family":"Zuliang","sequence":"additional","affiliation":[]},{"given":"Zhong","family":"Weizhou","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,4,5]]},"reference":[{"key":"e_1_2_7_1_2","article-title":"On a class of differential equations","volume":"10","author":"Vessiot E.","year":"1893","journal-title":"Annales Scientifiques de l\u2032\u00c9cole Normale Sup\u00e9rieure"},{"key":"e_1_2_7_2_2","article-title":"On differential equations possessing a fundamental system of integrals","volume":"116","author":"Guldberg A.","year":"1893","journal-title":"Comptes Rendus de l\u2032Acad\u00e9mie des Sciences"},{"key":"e_1_2_7_3_2","first-page":"71","article-title":"General studies on differential equations admitting finite continuous groups","volume":"25","author":"Lie S.","year":"1885","journal-title":"Mathematische Annalen"},{"key":"e_1_2_7_4_2","article-title":"On ordinary differential equations possessing fundamental systems of integrals","volume":"116","author":"Lie S.","year":"1893","journal-title":"Comptes Rendus de l\u2032Acad\u00e9mie des Sciences"},{"key":"e_1_2_7_5_2","unstructured":"TempleG. A superposition for ordinary differential equationns Lect. Topics in Nonlinear D.E. Report 1960 no. 1415 David Taylor Model Basin Carderock Md USA."},{"key":"e_1_2_7_6_2","unstructured":"InselbergA. On classification and superposition principles for nonlinear operators Ph.D. thesis 1965 University of Illinois at Urbana-Champaign Champaign Ill USA."},{"key":"e_1_2_7_7_2","unstructured":"IbragimovN. H. Discussion of Lie\u2019s nonlinear superposition theory Proceedings of the International Conference of Modern Group Analysis for the New Millennium (MOGRAN \u203200) October 2000 Ufa Russia."},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(67)90135-7"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(70)90080-6"},{"key":"e_1_2_7_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(70)90192-7"},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(70)90193-9"},{"key":"e_1_2_7_12_2","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.49.771"},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0274-2"},{"key":"e_1_2_7_14_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4757-4307-4"},{"key":"e_1_2_7_15_2","doi-asserted-by":"publisher","DOI":"10.1006\/jmaa.1997.5604"},{"key":"e_1_2_7_16_2","doi-asserted-by":"publisher","DOI":"10.1063\/1.530070"},{"key":"e_1_2_7_17_2","doi-asserted-by":"publisher","DOI":"10.1137\/0514042"},{"key":"e_1_2_7_18_2","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160030302"},{"key":"e_1_2_7_19_2","doi-asserted-by":"publisher","DOI":"10.1090\/qam\/42889"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/346824.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2012\/346824.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/2012\/346824","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,6,11]],"date-time":"2024-06-11T06:42:17Z","timestamp":1718088137000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/2012\/346824"}},"subtitle":[],"editor":[{"given":"B. V.","family":"Rathish Kumar","sequence":"additional","affiliation":[]}],"short-title":[],"issued":{"date-parts":[[2012,1]]},"references-count":19,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,1]]}},"alternative-id":["10.1155\/2012\/346824"],"URL":"https:\/\/doi.org\/10.1155\/2012\/346824","archive":["Portico"],"relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2012,1]]},"assertion":[{"value":"2011-11-29","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-01-31","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2012-04-05","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}],"article-number":"346824"}}