{"title":"以Burgers方程为代表的(3+1)维非线性偏微分方程的painlev<s:1>分析、Bäcklund变换和精确解","authors":"M.H.M. Moussa, Zidan M. Abd Al-Halim","doi":"10.1016/j.exco.2022.100081","DOIUrl":null,"url":null,"abstract":"<div><p>Herein, the Painlevé analysis and Bäcklund transformation for the (3+1) dimensional Burger equation are presented. Using this analysis, it is shown that the equation under consideration non-integrable. But, it is under a constraint equation may be integrable. We construct the Bäcklund transformation for that equation. Similarity solutions for the mentioned equation have been obtained. Some of these solutions are completely new.</p></div>","PeriodicalId":100517,"journal":{"name":"Examples and Counterexamples","volume":"2 ","pages":"Article 100081"},"PeriodicalIF":0.0000,"publicationDate":"2022-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2666657X22000179/pdfft?md5=007e91f8e4bfa868782a7c5be15704e5&pid=1-s2.0-S2666657X22000179-main.pdf","citationCount":"2","resultStr":"{\"title\":\"Painlevé analysis, Bäcklund transformation and Exact solutions for the (3+1)-dimensional nonlinear partial differential equation represented by Burgers’ equation\",\"authors\":\"M.H.M. Moussa, Zidan M. Abd Al-Halim\",\"doi\":\"10.1016/j.exco.2022.100081\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Herein, the Painlevé analysis and Bäcklund transformation for the (3+1) dimensional Burger equation are presented. Using this analysis, it is shown that the equation under consideration non-integrable. But, it is under a constraint equation may be integrable. We construct the Bäcklund transformation for that equation. Similarity solutions for the mentioned equation have been obtained. Some of these solutions are completely new.</p></div>\",\"PeriodicalId\":100517,\"journal\":{\"name\":\"Examples and Counterexamples\",\"volume\":\"2 \",\"pages\":\"Article 100081\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S2666657X22000179/pdfft?md5=007e91f8e4bfa868782a7c5be15704e5&pid=1-s2.0-S2666657X22000179-main.pdf\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Examples and Counterexamples\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S2666657X22000179\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Examples and Counterexamples","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S2666657X22000179","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Painlevé analysis, Bäcklund transformation and Exact solutions for the (3+1)-dimensional nonlinear partial differential equation represented by Burgers’ equation
Herein, the Painlevé analysis and Bäcklund transformation for the (3+1) dimensional Burger equation are presented. Using this analysis, it is shown that the equation under consideration non-integrable. But, it is under a constraint equation may be integrable. We construct the Bäcklund transformation for that equation. Similarity solutions for the mentioned equation have been obtained. Some of these solutions are completely new.
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