{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:58Z","timestamp":1740134578136,"version":"3.37.3"},"reference-count":15,"publisher":"Wiley","license":[{"start":{"date-parts":[[2014,1,1]],"date-time":"2014-01-01T00:00:00Z","timestamp":1388534400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2014]]},"abstract":"<jats:p>Complex Lie point transformations are used to linearize a class of systems of second order ordinary differential equations (ODEs) which have Lie algebras of maximum dimension<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>d<\/mml:mi><\/mml:mrow><\/mml:math>, with<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mi>d<\/mml:mi><mml:mo>\u2264<\/mml:mo><mml:mn>4<\/mml:mn><\/mml:math>. We identify such a class by employing complex structure on the manifold that defines the geometry of differential equations. Furthermore we provide a geometrical construction of the procedure adopted that provides an analogue in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>3<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>of the linearizability criteria in<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M4\"><mml:mrow><mml:msup><mml:mrow><mml:mi mathvariant=\"double-struck\">R<\/mml:mi><\/mml:mrow><mml:mrow><mml:mn>2<\/mml:mn><\/mml:mrow><\/mml:msup><\/mml:mrow><\/mml:math>.<\/jats:p>","DOI":"10.1155\/2014\/793247","type":"journal-article","created":{"date-parts":[[2014,11,19]],"date-time":"2014-11-19T23:42:18Z","timestamp":1416440538000},"page":"1-8","source":"Crossref","is-referenced-by-count":9,"title":["Linearization from Complex Lie Point Transformations"],"prefix":"10.1155","volume":"2014","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-8098-1897","authenticated-orcid":true,"given":"Sajid","family":"Ali","sequence":"first","affiliation":[{"name":"School of Electrical Engineering and Computer Science, National University of Sciences and Technology, Campus H-12, Islamabad 44000, Pakistan"}]},{"given":"M.","family":"Safdar","sequence":"additional","affiliation":[{"name":"School of Mechanical and Manufacturing Engineering, National University of Sciences and Technology, Campus H-12, Islamabad 44000, Pakistan"}]},{"given":"Asghar","family":"Qadir","sequence":"additional","affiliation":[{"name":"School of Natural Sciences, National University of Sciences and Technology, Campus H-12, Islamabad 44000, Pakistan"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-4350-2"},{"year":"1999","key":"2"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1112\/plms\/s3-71.1.221"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1063\/1.527948"},{"key":"5","doi-asserted-by":"publisher","DOI":"10.1142\/S1402925109000236"},{"key":"6","doi-asserted-by":"crossref","first-page":"631","DOI":"10.1070\/SM2010v201n05ABEH004085","volume":"201","year":"2010","journal-title":"Sbornik Mathematics"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1007\/s10440-006-9064-z"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.1088\/1751-8113\/43\/46\/465201"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1016\/j.jmaa.2013.08.033"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1088\/0305-4470\/27\/19\/004"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1098\/rspa.2009.0041"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1142\/S1402925112500131"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1023\/A:1008390431287"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/171834"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-010-9912-2"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/793247.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/793247.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2014\/793247.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2017,6,22]],"date-time":"2017-06-22T20:33:07Z","timestamp":1498163587000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2014\/793247\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"references-count":15,"alternative-id":["793247","793247"],"URL":"https:\/\/doi.org\/10.1155\/2014\/793247","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2014]]}}}