{"title":"李子代数的最优系统及非线性弹性杆方程的精确解。","authors":"Supriya Mondal, Arindam Ghosh, Sarit Maitra","doi":"10.1063/5.0254075","DOIUrl":null,"url":null,"abstract":"<p><p>The objective of this article is to find new traveling wave solutions of a celebrated nonlinear elastic rod (NER) equation with lateral inertia, describing the propagation of longitudinal waves through a nonlinear elastic rod by applying both the Lie point symmetry analysis and the first integral method. In order to determine the similarity reductions and invariant solutions, the Lie point symmetry analysis is applied to the NER equation and to this purpose, the invariants of the Lie algebra as well as a one-dimensional optimal system of subalgebras are constructed. Based on the members of the optimal system, similarity reductions and corresponding invariant solutions of the NER equation are derived. In addition, kink-shaped, anti-kink-shaped solitons, and a parabolic structure solution are obtained by solving the similarity reductions. Furthermore, we have found two new traveling wave solutions of the NER equation by applying the well-known first integral method. Using numerical results, the parametric dependence of the obtained solutions is also presented.</p>","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 5","pages":""},"PeriodicalIF":2.7000,"publicationDate":"2025-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimal system of Lie subalgebras and exact solutions of a nonlinear elastic rod equation.\",\"authors\":\"Supriya Mondal, Arindam Ghosh, Sarit Maitra\",\"doi\":\"10.1063/5.0254075\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>The objective of this article is to find new traveling wave solutions of a celebrated nonlinear elastic rod (NER) equation with lateral inertia, describing the propagation of longitudinal waves through a nonlinear elastic rod by applying both the Lie point symmetry analysis and the first integral method. In order to determine the similarity reductions and invariant solutions, the Lie point symmetry analysis is applied to the NER equation and to this purpose, the invariants of the Lie algebra as well as a one-dimensional optimal system of subalgebras are constructed. Based on the members of the optimal system, similarity reductions and corresponding invariant solutions of the NER equation are derived. In addition, kink-shaped, anti-kink-shaped solitons, and a parabolic structure solution are obtained by solving the similarity reductions. Furthermore, we have found two new traveling wave solutions of the NER equation by applying the well-known first integral method. Using numerical results, the parametric dependence of the obtained solutions is also presented.</p>\",\"PeriodicalId\":9974,\"journal\":{\"name\":\"Chaos\",\"volume\":\"35 5\",\"pages\":\"\"},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2025-05-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Chaos\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1063/5.0254075\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Chaos","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1063/5.0254075","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Optimal system of Lie subalgebras and exact solutions of a nonlinear elastic rod equation.
The objective of this article is to find new traveling wave solutions of a celebrated nonlinear elastic rod (NER) equation with lateral inertia, describing the propagation of longitudinal waves through a nonlinear elastic rod by applying both the Lie point symmetry analysis and the first integral method. In order to determine the similarity reductions and invariant solutions, the Lie point symmetry analysis is applied to the NER equation and to this purpose, the invariants of the Lie algebra as well as a one-dimensional optimal system of subalgebras are constructed. Based on the members of the optimal system, similarity reductions and corresponding invariant solutions of the NER equation are derived. In addition, kink-shaped, anti-kink-shaped solitons, and a parabolic structure solution are obtained by solving the similarity reductions. Furthermore, we have found two new traveling wave solutions of the NER equation by applying the well-known first integral method. Using numerical results, the parametric dependence of the obtained solutions is also presented.
期刊介绍:
Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.