{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,26]],"date-time":"2024-08-26T13:08:25Z","timestamp":1724677705643},"reference-count":62,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2017,7,11]],"date-time":"2017-07-11T00:00:00Z","timestamp":1499731200000},"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":"In this paper we make a Lie symmetry analysis of a generalized nonlinear beam equation with both second-order and fourth-order wave terms, which is extended from the classical beam equation arising in the historical events of travelling wave behavior in the Golden Gate Bridge in San Francisco. We perform a complete Lie symmetry group classification by using the equivalence transformation group theory for the equation under consideration. Lie symmetry reductions of a nonlinear beam-like equation which are singled out from the classification results are investigated. Some classes of exact solutions, including solitary wave solutions, triangular periodic wave solutions and rational solutions of the nonlinear beam-like equations are constructed by means of the reductions and symbolic computation.<\/jats:p>","DOI":"10.3390\/sym9070115","type":"journal-article","created":{"date-parts":[[2017,7,11]],"date-time":"2017-07-11T15:13:11Z","timestamp":1499785991000},"page":"115","source":"Crossref","is-referenced-by-count":4,"title":["Lie Symmetry Classification of the Generalized Nonlinear Beam Equation"],"prefix":"10.3390","volume":"9","author":[{"given":"Dingjiang","family":"Huang","sequence":"first","affiliation":[{"name":"Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China"},{"name":"School of Data Science and Engineering, East China Normal University, Shanghai 200062, China"}]},{"given":"Xiangxiang","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China"}]},{"given":"Shunchang","family":"Yu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China"}]}],"member":"1968","published-online":{"date-parts":[[2017,7,11]]},"reference":[{"key":"ref_1","unstructured":"Ames, W.F. 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