{"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":null,"pages":null},"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}
引用次数: 0
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.
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.
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