分数KdV类方程的对称性分析、不变解和守恒定律

IF 1 4区物理与天体物理 Q3 PHYSICS, MATHEMATICAL

Advances in Mathematical Physics Pub Date : 2022-10-28 DOI:10.1155/2022/5825938

Maria Ihsane El Bahi, K. Hilal

{"title":"分数KdV类方程的对称性分析、不变解和守恒定律","authors":"Maria Ihsane El Bahi, K. Hilal","doi":"10.1155/2022/5825938","DOIUrl":null,"url":null,"abstract":"In this paper, Lie symmetries of time-fractional KdV-Like equation with Riemann-Liouville derivative are performed. With the aid of infinitesimal symmetries, the vector fields and symmetry reductions of the equation are constructed, respectively; as a result, the invariant solutions are acquired in one case; we show that the KdV-like equation can be reduced to a fractional ordinary differential equation (FODE) which is connected with the Erdélyi-Kober functional derivative; for this kind of reduced form, we use the power series method for extracting the explicit solutions in the form of power series solution. Finally, Ibragimov’s theorem has been employed to construct the conservation laws.","PeriodicalId":49111,"journal":{"name":"Advances in Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2022-10-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation\",\"authors\":\"Maria Ihsane El Bahi, K. Hilal\",\"doi\":\"10.1155/2022/5825938\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, Lie symmetries of time-fractional KdV-Like equation with Riemann-Liouville derivative are performed. With the aid of infinitesimal symmetries, the vector fields and symmetry reductions of the equation are constructed, respectively; as a result, the invariant solutions are acquired in one case; we show that the KdV-like equation can be reduced to a fractional ordinary differential equation (FODE) which is connected with the Erdélyi-Kober functional derivative; for this kind of reduced form, we use the power series method for extracting the explicit solutions in the form of power series solution. Finally, Ibragimov’s theorem has been employed to construct the conservation laws.\",\"PeriodicalId\":49111,\"journal\":{\"name\":\"Advances in Mathematical Physics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.0000,\"publicationDate\":\"2022-10-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Advances in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://doi.org/10.1155/2022/5825938\",\"RegionNum\":4,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Advances in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1155/2022/5825938","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}

引用次数: 1

摘要

研究了一类具有Riemann-Liouville导数的时间分数阶类kdv方程的Lie对称性。借助于无穷小对称，分别构造了方程的向量场和对称约简;结果，在一种情况下得到了不变解;我们证明了类kdv方程可以简化为一个分数阶常微分方程(FODE)，该方程与erd - kober泛函导数有关;对于这种简化形式，我们使用幂级数方法来提取幂级数解形式的显式解。最后，利用伊布拉吉莫夫定理构造了守恒定律。

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

Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation

In this paper, Lie symmetries of time-fractional KdV-Like equation with Riemann-Liouville derivative are performed. With the aid of infinitesimal symmetries, the vector fields and symmetry reductions of the equation are constructed, respectively; as a result, the invariant solutions are acquired in one case; we show that the KdV-like equation can be reduced to a fractional ordinary differential equation (FODE) which is connected with the Erdélyi-Kober functional derivative; for this kind of reduced form, we use the power series method for extracting the explicit solutions in the form of power series solution. Finally, Ibragimov’s theorem has been employed to construct the conservation laws.

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

Advances in Mathematical Physics 数学-应用数学

CiteScore

2.40

自引率

8.30%

发文量

151

审稿时长

>12 weeks

期刊介绍： Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches. The journal welcomes submissions from mathematical physicists, theoretical physicists, and mathematicians alike. As well as original research, Advances in Mathematical Physics also publishes focused review articles that examine the state of the art, identify emerging trends, and suggest future directions for developing fields.