{"title":"Symmetries and Invariant Solutions of Higher-Order Evolution Systems","authors":"Rita Tracinà","doi":"10.3390/sym16081023","DOIUrl":null,"url":null,"abstract":"In this paper, we investigate evolution systems in two components, characterized by higher-order spatial derivatives and the presence of two arbitrary functions. Our study begins with an analysis of a fourth-order system. We perform a detailed group classification and identify specific forms of the constitutive functions that allow the system to exhibit additional symmetries in addition to spatial and temporal translations. We extend these results to nth-order systems. Moreover, we derive invariant solutions for these systems. Finally, for each order n, we are able to find non-negative solutions.","PeriodicalId":501198,"journal":{"name":"Symmetry","volume":"21 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Symmetry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3390/sym16081023","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we investigate evolution systems in two components, characterized by higher-order spatial derivatives and the presence of two arbitrary functions. Our study begins with an analysis of a fourth-order system. We perform a detailed group classification and identify specific forms of the constitutive functions that allow the system to exhibit additional symmetries in addition to spatial and temporal translations. We extend these results to nth-order systems. Moreover, we derive invariant solutions for these systems. Finally, for each order n, we are able to find non-negative solutions.
在本文中，我们研究了由两个部分组成的进化系统，其特点是具有高阶空间导数和存在两个任意函数。我们的研究从分析一个四阶系统开始。我们进行了详细的分组分类，并确定了构成函数的特定形式，使系统除了空间和时间平移外，还表现出额外的对称性。我们将这些结果扩展到 n 阶系统。此外，我们还得出了这些系统的不变解。最后，对于每个 n 阶，我们都能找到非负解。
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