{"title":"与第六个painlev<s:1>方程有关的离散系统","authors":"A. Ramani, Y. Ohta, B. Grammaticos","doi":"10.1088/0305-4470/39/39/S10","DOIUrl":null,"url":null,"abstract":"We present discrete Painlevé equations which can be obtained as contiguity relations of the solutions of the continuous Painlevé VI. The derivation is based on the geometry of the affine Weyl group D(1)4 associated with the bilinear formalism. As an offshoot we also present the contiguity relations of the solutions of the Bureau–Ablowitz–Fokas equation, which is a Miura transformed, ‘modified’, PVI.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Discrete systems related to the sixth Painlevé equation\",\"authors\":\"A. Ramani, Y. Ohta, B. Grammaticos\",\"doi\":\"10.1088/0305-4470/39/39/S10\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present discrete Painlevé equations which can be obtained as contiguity relations of the solutions of the continuous Painlevé VI. The derivation is based on the geometry of the affine Weyl group D(1)4 associated with the bilinear formalism. As an offshoot we also present the contiguity relations of the solutions of the Bureau–Ablowitz–Fokas equation, which is a Miura transformed, ‘modified’, PVI.\",\"PeriodicalId\":87442,\"journal\":{\"name\":\"Journal of physics A: Mathematical and general\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of physics A: Mathematical and general\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1088/0305-4470/39/39/S10\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of physics A: Mathematical and general","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1088/0305-4470/39/39/S10","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Discrete systems related to the sixth Painlevé equation
We present discrete Painlevé equations which can be obtained as contiguity relations of the solutions of the continuous Painlevé VI. The derivation is based on the geometry of the affine Weyl group D(1)4 associated with the bilinear formalism. As an offshoot we also present the contiguity relations of the solutions of the Bureau–Ablowitz–Fokas equation, which is a Miura transformed, ‘modified’, PVI.
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