{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:11:25Z","timestamp":1760238685995,"version":"build-2065373602"},"reference-count":25,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2020,8,18]],"date-time":"2020-08-18T00:00:00Z","timestamp":1597708800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this paper, we mainly put the Lie symmetry analysis method on the Gibbons-Tsarev equation (GTe) to obtain some new results, including some Lie symmetries, one-parameter transformation groups, explicit invariant solutions in the form of power series. Subsequently, the self-adjointness of the GTe is singled out. It follows that the conservation laws associated with symmetries of GTe are constructed with the aid of Ibragimov\u2019 method. Finally, we present the B\u00e4cklund transformations so that more abundant solutions can be worked out.<\/jats:p>","DOI":"10.3390\/sym12081378","type":"journal-article","created":{"date-parts":[[2020,8,19]],"date-time":"2020-08-19T21:37:40Z","timestamp":1597873060000},"page":"1378","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Lie Symmetry Analysis, Exact Solutions, Conservation Laws and B\u00e4cklund Transformations of the Gibbons-Tsarev Equation"],"prefix":"10.3390","volume":"12","author":[{"given":"Huanhuan","family":"Lu","sequence":"first","affiliation":[{"name":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yufeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,8,18]]},"reference":[{"key":"ref_1","unstructured":"Olver, P.J. 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