李代数与双曲守恒定律

IF 0.5 2区数学 Q3 MATHEMATICS

International Journal of Algebra and Computation Pub Date : 2022-01-01 DOI:10.12988/ija.2022.91731

Yacine Benhadid, Yousuf Alkhezi

{"title":"李代数与双曲守恒定律","authors":"Yacine Benhadid, Yousuf Alkhezi","doi":"10.12988/ija.2022.91731","DOIUrl":null,"url":null,"abstract":"A general implementation is presented for constructing the relation between the conservation laws for partial diﬀerential equations and the Lie algebra. This construction does not require the use of existence of a variational principle and reduces the calculation of conservation laws to solving a system of linear determining equations similar to that for ﬁnding symmetries. An explicit formula is derived which yields a conservation law for each solution of the determining system. A simulation of this combination to solve partial diﬀerential equation is elaborated by an application on Burger’s equation which shows several results. General behavior of the distribution function for conservation laws of these equations are obtained and shown.","PeriodicalId":13756,"journal":{"name":"International Journal of Algebra and Computation","volume":"28 1","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Lie algebras and hyperbolic conservation laws\",\"authors\":\"Yacine Benhadid, Yousuf Alkhezi\",\"doi\":\"10.12988/ija.2022.91731\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A general implementation is presented for constructing the relation between the conservation laws for partial diﬀerential equations and the Lie algebra. This construction does not require the use of existence of a variational principle and reduces the calculation of conservation laws to solving a system of linear determining equations similar to that for ﬁnding symmetries. An explicit formula is derived which yields a conservation law for each solution of the determining system. A simulation of this combination to solve partial diﬀerential equation is elaborated by an application on Burger’s equation which shows several results. General behavior of the distribution function for conservation laws of these equations are obtained and shown.\",\"PeriodicalId\":13756,\"journal\":{\"name\":\"International Journal of Algebra and Computation\",\"volume\":\"28 1\",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2022-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Algebra and Computation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.12988/ija.2022.91731\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Algebra and Computation","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.12988/ija.2022.91731","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 0

摘要

给出了构造偏微分方程守恒律与李代数之间关系的一般实现。这种构造不需要使用变分原理的存在性，并且将守恒定律的计算简化为求解一个类似于寻找对称性的线性确定方程组的系统。导出了一个显式公式，该公式为决定系统的每个解提供了守恒定律。通过在伯格方程上的应用，对这种组合求解偏微分方程进行了模拟，得到了几个结果。给出了这些方程守恒律的分布函数的一般性质。

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

Lie algebras and hyperbolic conservation laws

A general implementation is presented for constructing the relation between the conservation laws for partial diﬀerential equations and the Lie algebra. This construction does not require the use of existence of a variational principle and reduces the calculation of conservation laws to solving a system of linear determining equations similar to that for ﬁnding symmetries. An explicit formula is derived which yields a conservation law for each solution of the determining system. A simulation of this combination to solve partial diﬀerential equation is elaborated by an application on Burger’s equation which shows several results. General behavior of the distribution function for conservation laws of these equations are obtained and shown.

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

International Journal of Algebra and Computation 数学-数学

CiteScore

1.20

自引率

12.50%

发文量

审稿时长

6-12 weeks

期刊介绍： The International Journal of Algebra and Computation publishes high quality original research papers in combinatorial, algorithmic and computational aspects of algebra (including combinatorial and geometric group theory and semigroup theory, algorithmic aspects of universal algebra, computational and algorithmic commutative algebra, probabilistic models related to algebraic structures, random algebraic structures), and gives a preference to papers in the areas of mathematics represented by the editorial board.