第二类广义Lane-Emden方程的精确解

IF 0.6 4区数学 Q4 MATHEMATICS, APPLIED

Applications of Mathematics Pub Date : 2024-09-13 DOI:10.21136/AM.2024.0220-23

Kismet Kasapoǧlu

{"title":"第二类广义Lane-Emden方程的精确解","authors":"Kismet Kasapoǧlu","doi":"10.21136/AM.2024.0220-23","DOIUrl":null,"url":null,"abstract":"<div><p>Contact and Lie point symmetries of a certain class of second order differential equations using the Lie symmetry theory are obtained. Generators of these symmetries are used to obtain first integrals and exact solutions of the equations. This class of equations is transformed into the so-called generalized Lane-Emden equations of the second kind</p><div><div><span>$$y^{\\prime\\prime}(x)+{k\\over{x}}y^{\\prime}(x)+ g(x){\\rm {e}}^{ny}=0.$$</span></div></div><p>Then we consider two types of functions <i>g</i>(<i>x</i>) and present first integrals and exact solutions of the Lane-Emden equation for them. One of the considered cases is new.</p></div>","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"69 6","pages":"747 - 755"},"PeriodicalIF":0.6000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exact solutions of generalized Lane-Emden equations of the second kind\",\"authors\":\"Kismet Kasapoǧlu\",\"doi\":\"10.21136/AM.2024.0220-23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Contact and Lie point symmetries of a certain class of second order differential equations using the Lie symmetry theory are obtained. Generators of these symmetries are used to obtain first integrals and exact solutions of the equations. This class of equations is transformed into the so-called generalized Lane-Emden equations of the second kind</p><div><div><span>$$y^{\\\\prime\\\\prime}(x)+{k\\\\over{x}}y^{\\\\prime}(x)+ g(x){\\\\rm {e}}^{ny}=0.$$</span></div></div><p>Then we consider two types of functions <i>g</i>(<i>x</i>) and present first integrals and exact solutions of the Lane-Emden equation for them. One of the considered cases is new.</p></div>\",\"PeriodicalId\":55505,\"journal\":{\"name\":\"Applications of Mathematics\",\"volume\":\"69 6\",\"pages\":\"747 - 755\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Applications of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://link.springer.com/article/10.21136/AM.2024.0220-23\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Applications of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.21136/AM.2024.0220-23","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}

引用次数: 0

摘要

利用李对称理论，得到了一类二阶微分方程的接触点对称性和李点对称性。这些对称的产生器被用来得到方程的第一积分和精确解。将这类方程转化为所谓的广义第二类Lane-Emden方程$$y^{\prime\prime}(x)+{k\over{x}}y^{\prime}(x)+ g(x){\rm {e}}^{ny}=0.$$然后考虑两类函数g(x)，给出它们的第一积分和Lane-Emden方程的精确解。其中一个被考虑的案例是新的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Exact solutions of generalized Lane-Emden equations of the second kind

Contact and Lie point symmetries of a certain class of second order differential equations using the Lie symmetry theory are obtained. Generators of these symmetries are used to obtain first integrals and exact solutions of the equations. This class of equations is transformed into the so-called generalized Lane-Emden equations of the second kind

$$y^{\prime\prime}(x)+{k\over{x}}y^{\prime}(x)+ g(x){\rm {e}}^{ny}=0.$$

Then we consider two types of functions g(x) and present first integrals and exact solutions of the Lane-Emden equation for them. One of the considered cases is new.

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

Applications of Mathematics 数学-应用数学

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

3.0 months

期刊介绍： Applications of Mathematics publishes original high quality research papers that are directed towards applications of mathematical methods in various branches of science and engineering. The main topics covered include: - Mechanics of Solids; - Fluid Mechanics; - Electrical Engineering; - Solutions of Differential and Integral Equations; - Mathematical Physics; - Optimization; - Probability Mathematical Statistics. The journal is of interest to a wide audience of mathematicians, scientists and engineers concerned with the development of scientific computing, mathematical statistics and applicable mathematics in general.