{"title":"埃姆登-李纳方程的非线性类分析","authors":"M. Ahmed, A. H. Kara","doi":"10.1007/s13370-025-01279-9","DOIUrl":null,"url":null,"abstract":"<div><p>We present a general method to construct first integrals for some classes of the well known second-order ordinary differential equations, viz., the Emden and Liénard classes of equations. The approach does not require a knowledge of a Lagrangian but, rather, uses the ‘multiplier approach’ [1, 2]. It is then shown how a study of the invariance properties and conservation laws are used to ‘twice’ reduce the equations to solutions. In this paper, we restrict our work to the nonlinearizable cases.</p></div>","PeriodicalId":46107,"journal":{"name":"Afrika Matematika","volume":"36 2","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2025-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s13370-025-01279-9.pdf","citationCount":"0","resultStr":"{\"title\":\"An analysis of the nonlinearizable classes of Emden-Liénard equations\",\"authors\":\"M. Ahmed, A. H. Kara\",\"doi\":\"10.1007/s13370-025-01279-9\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We present a general method to construct first integrals for some classes of the well known second-order ordinary differential equations, viz., the Emden and Liénard classes of equations. The approach does not require a knowledge of a Lagrangian but, rather, uses the ‘multiplier approach’ [1, 2]. It is then shown how a study of the invariance properties and conservation laws are used to ‘twice’ reduce the equations to solutions. In this paper, we restrict our work to the nonlinearizable cases.</p></div>\",\"PeriodicalId\":46107,\"journal\":{\"name\":\"Afrika Matematika\",\"volume\":\"36 2\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2025-03-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s13370-025-01279-9.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Afrika Matematika\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s13370-025-01279-9\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Afrika Matematika","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1007/s13370-025-01279-9","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
An analysis of the nonlinearizable classes of Emden-Liénard equations
We present a general method to construct first integrals for some classes of the well known second-order ordinary differential equations, viz., the Emden and Liénard classes of equations. The approach does not require a knowledge of a Lagrangian but, rather, uses the ‘multiplier approach’ [1, 2]. It is then shown how a study of the invariance properties and conservation laws are used to ‘twice’ reduce the equations to solutions. In this paper, we restrict our work to the nonlinearizable cases.
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