李子代数的最优系统及非线性弹性杆方程的精确解。

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2025-05-01 DOI:10.1063/5.0254075
Supriya Mondal, Arindam Ghosh, Sarit Maitra
{"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}
引用次数: 0

摘要

本文的目的是寻找具有横向惯性的著名非线性弹性杆方程的新的行波解,用李点对称分析和第一次积分方法来描述纵波在非线性弹性杆中的传播。为了确定NER方程的相似约简和不变解,将李点对称分析应用于NER方程,并为此构造了李代数的不变量和一维最优子代数系统。根据最优系统的成员,导出了NER方程的相似约简和相应的不变解。此外,通过求解相似约简得到了扭结孤子、反扭结孤子和抛物型结构解。此外,我们利用著名的第一次积分方法,找到了NER方程的两个新的行波解。利用数值结果,给出了解的参数依赖性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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.

求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
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.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信