{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,29]],"date-time":"2025-11-29T16:23:02Z","timestamp":1764433382535,"version":"3.40.5"},"reference-count":38,"publisher":"Wiley","license":[{"start":{"date-parts":[[2020,8,28]],"date-time":"2020-08-28T00:00:00Z","timestamp":1598572800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Complexity"],"published-print":{"date-parts":[[2020,8,28]]},"abstract":"<jats:p>Nonlinear evolution equations widely describe phenomena in various fields of science, such as plasma, nuclear physics, chemical reactions, optics, shallow water waves, fluid dynamics, signal processing, and image processing. In the present work, the derivation and analysis of Lie symmetries are presented for the time-fractional Benjamin\u2013Bona\u2013Mahony equation (FBBM) with the Riemann\u2013Liouville derivatives. The time FBBM equation is reduced to a nonlinear fractional ordinary differential equation (NLFODE) using its Lie symmetries. These symmetries are derivations using the prolongation theorem. Applying the subequation method, we then use the integrating factor property to solve the NLFODE to obtain a few travelling wave solutions to the time FBBM.<\/jats:p>","DOI":"10.1155\/2020\/3714832","type":"journal-article","created":{"date-parts":[[2020,8,29]],"date-time":"2020-08-29T00:25:57Z","timestamp":1598660757000},"page":"1-8","source":"Crossref","is-referenced-by-count":12,"title":["Analytical Solutions for Nonlinear Dispersive Physical Model"],"prefix":"10.1155","volume":"2020","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5309-1493","authenticated-orcid":true,"given":"Wen-Xiu","family":"Ma","sequence":"first","affiliation":[{"name":"Department of Mathematics, Zhejiang Normal University, Jinhua 321004, Zhejiang, China"},{"name":"Department of Mathematics, King Abdulaziz University, Jeddah 21589, Saudi Arabia"},{"name":"Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620-5700, USA"},{"name":"School of Mathematics, South China University of Technology, Guangzhou 510640, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0795-0709","authenticated-orcid":true,"given":"Mohamed R.","family":"Ali","sequence":"additional","affiliation":[{"name":"Department of Basic Science, Faculty of Engineering at Benha, Benha University, 13512, Egypt"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6954-5517","authenticated-orcid":true,"given":"R.","family":"Sadat","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Zagazig Faculty of Engineering, Zagazig University, Zagazig, Egypt"}]}],"member":"311","reference":[{"key":"1","doi-asserted-by":"publisher","DOI":"10.1007\/s11082-020-02412-7"},{"key":"2","doi-asserted-by":"publisher","DOI":"10.1007\/s11082-019-2162-8"},{"key":"3","doi-asserted-by":"publisher","DOI":"10.1007\/s11082-019-1813-0"},{"key":"4","doi-asserted-by":"publisher","DOI":"10.1007\/s11082-019-1801-4"},{"key":"6","doi-asserted-by":"publisher","DOI":"10.1016\/j.cjph.2020.01.008"},{"key":"7","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/9801638"},{"key":"8","doi-asserted-by":"publisher","DOI":"10.2298\/tsci190101292a"},{"key":"9","doi-asserted-by":"publisher","DOI":"10.1155\/2019\/3456848"},{"key":"10","doi-asserted-by":"publisher","DOI":"10.1016\/j.rinp.2018.11.056"},{"key":"11","doi-asserted-by":"publisher","DOI":"10.1002\/mma.6001"},{"key":"12","doi-asserted-by":"publisher","DOI":"10.1016\/j.matcom.2020.01.005"},{"key":"13","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2019.124605"},{"key":"14","doi-asserted-by":"publisher","DOI":"10.3233\/jifs-179813"},{"key":"15","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2015.12.014"},{"key":"16","doi-asserted-by":"publisher","DOI":"10.1140\/epjp\/i2019-12808-6"},{"key":"17","doi-asserted-by":"publisher","DOI":"10.1142\/s0218348x95000497"},{"key":"18","doi-asserted-by":"publisher","DOI":"10.1186\/s13662-019-2336-5"},{"key":"19","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2012.05.013"},{"key":"20","doi-asserted-by":"publisher","DOI":"10.1088\/1402-4896\/ab48c1"},{"year":"1974","key":"21"},{"key":"22","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2015.06.008"},{"key":"23","doi-asserted-by":"publisher","DOI":"10.15388\/na.2017.6.9"},{"key":"24","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2017.11.015"},{"key":"25","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2012.11.032"},{"key":"26","doi-asserted-by":"publisher","DOI":"10.1016\/j.physa.2017.10.010"},{"key":"27","doi-asserted-by":"publisher","DOI":"10.1002\/mma.4254"},{"key":"28","doi-asserted-by":"publisher","DOI":"10.1155\/2014\/217184"},{"key":"29","doi-asserted-by":"publisher","DOI":"10.1088\/1361-6544\/aa99a2"},{"key":"30","doi-asserted-by":"publisher","DOI":"10.1186\/1687-1847-2014-228"},{"key":"31","doi-asserted-by":"publisher","DOI":"10.1016\/j.camwa.2017.12.001"},{"key":"32","doi-asserted-by":"publisher","DOI":"10.1007\/s11071-013-1150-y"},{"issue":"3","key":"33","first-page":"21","volume":"9","year":"2007","journal-title":"Vestnik Usatu"},{"year":"2000","key":"34"},{"key":"35","doi-asserted-by":"publisher","DOI":"10.1016\/j.cpc.2013.09.019"},{"key":"36","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2014.01.002"},{"year":"1993","key":"37"},{"key":"38","doi-asserted-by":"publisher","DOI":"10.1007\/s10092-015-0158-8"},{"key":"39","doi-asserted-by":"publisher","DOI":"10.1016\/j.physleta.2011.01.029"}],"container-title":["Complexity"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/3714832.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/3714832.xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/downloads.hindawi.com\/journals\/complexity\/2020\/3714832.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,8,29]],"date-time":"2020-08-29T00:25:59Z","timestamp":1598660759000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.hindawi.com\/journals\/complexity\/2020\/3714832\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,8,28]]},"references-count":38,"alternative-id":["3714832","3714832"],"URL":"https:\/\/doi.org\/10.1155\/2020\/3714832","relation":{},"ISSN":["1076-2787","1099-0526"],"issn-type":[{"type":"print","value":"1076-2787"},{"type":"electronic","value":"1099-0526"}],"subject":[],"published":{"date-parts":[[2020,8,28]]}}}