{"title":"(1+3)维齐次monge - ampantere方程的对称约简及若干类不变解","authors":"V. Fedorchuk, V. Fedorchuk","doi":"10.15673/tmgc.v14i3.2078","DOIUrl":null,"url":null,"abstract":"We study the relationship between structural properties of the two-dimensional nonconjugate subalgebras of the same rank of the Lie algebra of the Poincaré group P(1,4) and the properties of reduced equations for the (1+3)-dimensional homogeneous Monge-Ampère equation. In this paper, we present some of the results obtained concerning symmetry reduction of the equation under investigation to identities. Some classes of the invariant solutions (with arbitrary smooth functions) are presented.","PeriodicalId":36547,"journal":{"name":"Proceedings of the International Geometry Center","volume":"321 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2021-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On symmetry reduction and some classes of invariant solutions of the (1+3)-dimensional homogeneous Monge-Ampère equation\",\"authors\":\"V. Fedorchuk, V. Fedorchuk\",\"doi\":\"10.15673/tmgc.v14i3.2078\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the relationship between structural properties of the two-dimensional nonconjugate subalgebras of the same rank of the Lie algebra of the Poincaré group P(1,4) and the properties of reduced equations for the (1+3)-dimensional homogeneous Monge-Ampère equation. In this paper, we present some of the results obtained concerning symmetry reduction of the equation under investigation to identities. Some classes of the invariant solutions (with arbitrary smooth functions) are presented.\",\"PeriodicalId\":36547,\"journal\":{\"name\":\"Proceedings of the International Geometry Center\",\"volume\":\"321 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-12-24\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the International Geometry Center\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.15673/tmgc.v14i3.2078\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the International Geometry Center","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.15673/tmgc.v14i3.2078","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
On symmetry reduction and some classes of invariant solutions of the (1+3)-dimensional homogeneous Monge-Ampère equation
We study the relationship between structural properties of the two-dimensional nonconjugate subalgebras of the same rank of the Lie algebra of the Poincaré group P(1,4) and the properties of reduced equations for the (1+3)-dimensional homogeneous Monge-Ampère equation. In this paper, we present some of the results obtained concerning symmetry reduction of the equation under investigation to identities. Some classes of the invariant solutions (with arbitrary smooth functions) are presented.
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