{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,20]],"date-time":"2026-05-20T21:25:05Z","timestamp":1779312305777,"version":"3.51.4"},"reference-count":30,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,6,25]],"date-time":"2022-06-25T00:00:00Z","timestamp":1656115200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12105073"],"award-info":[{"award-number":["12105073"]}]},{"name":"National Natural Science Foundation of China","award":["QN2020144"],"award-info":[{"award-number":["QN2020144"]}]},{"name":"National Natural Science Foundation of China","award":["2020YB15"],"award-info":[{"award-number":["2020YB15"]}]},{"name":"National Natural Science Foundation of China","award":["1020708"],"award-info":[{"award-number":["1020708"]}]},{"name":"Science and Technology Program of Colleges and Universities in Hebei Province","award":["12105073"],"award-info":[{"award-number":["12105073"]}]},{"name":"Science and Technology Program of Colleges and Universities in Hebei Province","award":["QN2020144"],"award-info":[{"award-number":["QN2020144"]}]},{"name":"Science and Technology Program of Colleges and Universities in Hebei Province","award":["2020YB15"],"award-info":[{"award-number":["2020YB15"]}]},{"name":"Science and Technology Program of Colleges and Universities in Hebei Province","award":["1020708"],"award-info":[{"award-number":["1020708"]}]},{"name":"Scientific Research and Development Program Fund Project of Hebei University of Economics and Business","award":["12105073"],"award-info":[{"award-number":["12105073"]}]},{"name":"Scientific Research and Development Program Fund Project of Hebei University of Economics and Business","award":["QN2020144"],"award-info":[{"award-number":["QN2020144"]}]},{"name":"Scientific Research and Development Program Fund Project of Hebei University of Economics and Business","award":["2020YB15"],"award-info":[{"award-number":["2020YB15"]}]},{"name":"Scientific Research and Development Program Fund Project of Hebei University of Economics and Business","award":["1020708"],"award-info":[{"award-number":["1020708"]}]},{"name":"Youth Team Support Program of Hebei University of Economics and Business","award":["12105073"],"award-info":[{"award-number":["12105073"]}]},{"name":"Youth Team Support Program of Hebei University of Economics and Business","award":["QN2020144"],"award-info":[{"award-number":["QN2020144"]}]},{"name":"Youth Team Support Program of Hebei University of Economics and Business","award":["2020YB15"],"award-info":[{"award-number":["2020YB15"]}]},{"name":"Youth Team Support Program of Hebei University of Economics and Business","award":["1020708"],"award-info":[{"award-number":["1020708"]}]},{"name":"Doctoral Research Start-up Fund project of Zaozhuang University","award":["12105073"],"award-info":[{"award-number":["12105073"]}]},{"name":"Doctoral Research Start-up Fund project of Zaozhuang University","award":["QN2020144"],"award-info":[{"award-number":["QN2020144"]}]},{"name":"Doctoral Research Start-up Fund project of Zaozhuang University","award":["2020YB15"],"award-info":[{"award-number":["2020YB15"]}]},{"name":"Doctoral Research Start-up Fund project of Zaozhuang University","award":["1020708"],"award-info":[{"award-number":["1020708"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, by applying the Lie group method and the direct symmetry method, Lie algebras of the Benjiamin Ono equation are obtained, and we find that results of the two methods are same. Based on the Lie algebra, Lie symmetry groups, relationships between new solutions and old solutions, two kinds of ODEs as symmetry reductions are obtained. Making use of the power series method, the exact power series solution of the Benjiamin Ono equation has been derived. We also give the conservation laws of Benjiamin Ono equation by means of Ibragimovs new conservation Theorem.<\/jats:p>","DOI":"10.3390\/sym14071315","type":"journal-article","created":{"date-parts":[[2022,6,26]],"date-time":"2022-06-26T22:50:23Z","timestamp":1656283823000},"page":"1315","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":6,"title":["Lie Symmetry Analysis, Particular Solutions and Conservation Laws of Benjiamin Ono Equation"],"prefix":"10.3390","volume":"14","author":[{"given":"Zhenli","family":"Wang","sequence":"first","affiliation":[{"name":"School of Mathematical and Statistics, Zaozhuang University, Zaozhuang 277160, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3544-8609","authenticated-orcid":false,"given":"Liangji","family":"Sun","sequence":"additional","affiliation":[{"name":"School of Mathematical and Statistics, Zaozhuang University, Zaozhuang 277160, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Rui","family":"Hua","sequence":"additional","affiliation":[{"name":"School of Mathematical and Statistics, Zaozhuang University, Zaozhuang 277160, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lihua","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematical and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Haifeng","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Science, Jimei University, Xiamen 361021, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,25]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"383","DOI":"10.1016\/S0375-9601(02)01516-5","article-title":"Applications of the Jacobi elliptic function method to special-type nonlinear equations","volume":"305","author":"Fan","year":"2002","journal-title":"Phys. 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