{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:43:02Z","timestamp":1740134582808,"version":"3.37.3"},"reference-count":18,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"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":[[2013]]},"abstract":"<jats:p>We find exact solutions of the Generalized Modified Boussinesq (GMB) equation, the Kuromoto-Sivashinsky (KS) equation the and, Camassa-Holm (CH) equation by utilizing the double reduction theory related to conserved vectors. The fourth order GMB equation involves the arbitrary function and mixed derivative terms in highest derivative. The partial Noether\u2019s approach yields seven conserved vectors for GMB equation and one conserved for vector KS equation. Due to presence of mixed derivative term the conserved vectors for GMB equation derived by the Noether like theorem do not satisfy the divergence relationship. The extra terms that constitute the trivial part of conserved vectors are adjusted and the resulting conserved vectors satisfy the divergence property. The double reduction theory yields two independent solutions and one reduction for GMB equation and one solution for KS equation. For CH equation two independent solutions are obtained elsewhere by double reduction theory with the help of conserved Vectors.<\/jats:p>","DOI":"10.1155\/2013\/902128","type":"journal-article","created":{"date-parts":[[2013,10,31]],"date-time":"2013-10-31T23:10:52Z","timestamp":1383261052000},"page":"1-8","source":"Crossref","is-referenced-by-count":3,"title":["Exact Solutions of Generalized Modified Boussinesq, Kuramoto-Sivashinsky, and Camassa-Holm Equations via Double Reduction Theory"],"prefix":"10.1155","volume":"2013","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9505-847X","authenticated-orcid":true,"given":"Zulfiqar","family":"Ali","sequence":"first","affiliation":[{"name":"Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Syed","family":"Husnine","sequence":"additional","affiliation":[{"name":"Department of Sciences and Humanities, National University of Computer and Emerging Sciences, Lahore Campus, Lahore 54000, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Imran","family":"Naeem","sequence":"additional","affiliation":[{"name":"Department of Mathematics, School of Science and Engineering, Lahore University of Management Sciences, Opposite Sector \u2018U,\u2019 DHA, Lahore 54792, Pakistan"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","reference":[{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0274-2"},{"year":"1973","key":"3"},{"year":"1989","key":"4"},{"volume":"1","volume-title":"CRC Handbook of Lie group analysis of differential equations","year":"1994","key":"5"},{"year":"1989","key":"6"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.06.002"},{"key":"8","first-page":"235","volume":"2","year":"1918","journal-title":"Nachrichten von der Gesellschaft der Wissenschaften zu G\u00f6ttingen, Mathematisch-Physikalische Klasse"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-005-9013-9"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2008.06.042"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1003686831523"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/S0096-3003(03)00259-5"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2004.10.006"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.06.059"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2008.09.029"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2009.10.009"},{"issue":"4","key":"17","doi-asserted-by":"crossref","first-page":"732","DOI":"10.3390\/mca15040732","volume":"15","year":"2010","journal-title":"Mathematical & Computational Applications"},{"key":"1","doi-asserted-by":"publisher","DOI":"10.1016\/j.nonrwa.2008.09.028"},{"key":"18","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/0378-4371(82)90266-7","volume":"114","year":"1982","journal-title":"Physica A"}],"container-title":["Journal of Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/902128.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/902128.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/jam\/2013\/902128.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,7,31]],"date-time":"2019-07-31T17:27:31Z","timestamp":1564594051000},"score":1,"resource":{"primary":{"URL":"http:\/\/www.hindawi.com\/journals\/jam\/2013\/902128\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013]]},"references-count":18,"alternative-id":["902128","902128"],"URL":"https:\/\/doi.org\/10.1155\/2013\/902128","relation":{},"ISSN":["1110-757X","1687-0042"],"issn-type":[{"type":"print","value":"1110-757X"},{"type":"electronic","value":"1687-0042"}],"subject":[],"published":{"date-parts":[[2013]]}}}