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The present study provides an extended method that is also applicable to partial differential equations. The main characteristic of the extended method is the restriction of the manifold by some constraint equations on which we search for a Lie symmetry group. This extension makes it possible to find a partial Lie symmetry group, which leads to a reduced dynamics describing the asymptotic behavior.<\/jats:p>","DOI":"10.1155\/2015\/601657","type":"journal-article","created":{"date-parts":[[2015,9,29]],"date-time":"2015-09-29T17:05:49Z","timestamp":1443546349000},"page":"1-8","source":"Crossref","is-referenced-by-count":1,"title":["Derivation of Asymptotic Dynamical Systems with Partial Lie Symmetry Groups"],"prefix":"10.1155","volume":"2015","author":[{"given":"Masatomo","family":"Iwasa","sequence":"first","affiliation":[{"name":"General Education Department, Aichi Institute of Technology, 1247 Yachigusa Yakusacho, Toyota 470-0392, Japan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"year":"1961","key":"1"},{"key":"2","first-page":"287","volume":"18","year":"1966","journal-title":"Publications of the Astronomical Society of Japan"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1143\/ptps.55.1"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"year":"1993","key":"5"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1143\/ptp.94.503"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/0378-4371(94)90421-9"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.54.376"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1143\/ptp.102.471"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.physd.2007.12.009"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1137\/070694892"},{"year":"1986","key":"12"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1070\/sm1989v064n02abeh003318"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/22\/18\/007"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/25\/18\/002"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1134\/s0012266107050035"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.2991\/jnmp.2007.14.2.1"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1134\/s0021894414020047"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1155\/MPE\/2006\/68753"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/27\/2\/027"},{"key":"21","doi-asserted-by":"publisher","DOI":"10.1103\/physreva.72.033419"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.2991\/jnmp.2005.12.s2.9"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.1142\/s0219887805000983"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.2991\/jnmp.2005.12.4.9"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1209\/0295-5075\/80\/60005"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1063\/1.532374"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1007\/bf02557382"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1007\/bf02557230"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1016\/s0370-1573(01)00039-4"},{"issue":"2","key":"30","first-page":"850","volume":"50","year":"2004","journal-title":"Proceedings of the Institute of Mathematics of NAS of Ukraine"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1143\/ptp.116.605"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/41\/8\/085204"},{"key":"33","doi-asserted-by":"publisher","DOI":"10.1063\/1.3097304"},{"key":"34","doi-asserted-by":"publisher","DOI":"10.1143\/ptp.100.199"},{"year":"1992","key":"35"},{"key":"36","doi-asserted-by":"publisher","DOI":"10.1002\/cpa.3160470606"},{"key":"37","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.66.046105"},{"key":"38","doi-asserted-by":"publisher","DOI":"10.1103\/physreve.72.046136"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/601657.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/601657.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2015\/601657.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2016,7,27]],"date-time":"2016-07-27T18:27:25Z","timestamp":1469644045000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2015\/601657\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015]]},"references-count":38,"alternative-id":["601657","601657"],"URL":"https:\/\/doi.org\/10.1155\/2015\/601657","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2015]]}}}