{"title":"非线性波动方程utt + ut = f(x, ux)uxx + g(x, ux)的初步群分类","authors":"T. Masebe","doi":"10.37394/232020.2022.2.22","DOIUrl":null,"url":null,"abstract":"The paper discusses the non-linear wave equations whose coefficients are dependent on first order spatial derivatives. We construct the principal Lie algebra, the equivalence Lie al- gebra, and the extensions by one of the princi- pal Lie algebra. We further construct the op- timal system of one-dimensional subalgebras for rst three extended five-dimensional Lie alge- bras. These are finally used to determine invari- ant solutions of some examples.","PeriodicalId":93382,"journal":{"name":"The international journal of evidence & proof","volume":"22 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Preliminary Group Classification of nonlinear wave equation utt + ut = f(x, ux)uxx + g(x, ux)\",\"authors\":\"T. Masebe\",\"doi\":\"10.37394/232020.2022.2.22\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The paper discusses the non-linear wave equations whose coefficients are dependent on first order spatial derivatives. We construct the principal Lie algebra, the equivalence Lie al- gebra, and the extensions by one of the princi- pal Lie algebra. We further construct the op- timal system of one-dimensional subalgebras for rst three extended five-dimensional Lie alge- bras. These are finally used to determine invari- ant solutions of some examples.\",\"PeriodicalId\":93382,\"journal\":{\"name\":\"The international journal of evidence & proof\",\"volume\":\"22 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"The international journal of evidence & proof\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.37394/232020.2022.2.22\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"The international journal of evidence & proof","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37394/232020.2022.2.22","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Preliminary Group Classification of nonlinear wave equation utt + ut = f(x, ux)uxx + g(x, ux)
The paper discusses the non-linear wave equations whose coefficients are dependent on first order spatial derivatives. We construct the principal Lie algebra, the equivalence Lie al- gebra, and the extensions by one of the princi- pal Lie algebra. We further construct the op- timal system of one-dimensional subalgebras for rst three extended five-dimensional Lie alge- bras. These are finally used to determine invari- ant solutions of some examples.
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