{"title":"复域中第二个painlevÉ方程的boutroux解析","authors":"V Yu Novokshënov","doi":"10.1070/IM1991V037N03ABEH002160","DOIUrl":null,"url":null,"abstract":"An asymptotic representation of the general solution of the second Painleve equation is constructed in a sector of the complex -plane. The principal term of the asymptotics is an elliptic function whose modulus and argument are functions of . Explicit expressions of these functions are given, and an approximation as is proved for the initial Painleve function outside a small neighborhood of its lattice of poles.","PeriodicalId":159459,"journal":{"name":"Mathematics of The Ussr-izvestiya","volume":"387 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"34","resultStr":"{\"title\":\"THE BOUTROUX ANSATZ FOR THE SECOND PAINLEVÉ EQUATION IN THE COMPLEX DOMAIN\",\"authors\":\"V Yu Novokshënov\",\"doi\":\"10.1070/IM1991V037N03ABEH002160\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"An asymptotic representation of the general solution of the second Painleve equation is constructed in a sector of the complex -plane. The principal term of the asymptotics is an elliptic function whose modulus and argument are functions of . Explicit expressions of these functions are given, and an approximation as is proved for the initial Painleve function outside a small neighborhood of its lattice of poles.\",\"PeriodicalId\":159459,\"journal\":{\"name\":\"Mathematics of The Ussr-izvestiya\",\"volume\":\"387 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1991-06-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"34\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematics of The Ussr-izvestiya\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1070/IM1991V037N03ABEH002160\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics of The Ussr-izvestiya","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1070/IM1991V037N03ABEH002160","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
THE BOUTROUX ANSATZ FOR THE SECOND PAINLEVÉ EQUATION IN THE COMPLEX DOMAIN
An asymptotic representation of the general solution of the second Painleve equation is constructed in a sector of the complex -plane. The principal term of the asymptotics is an elliptic function whose modulus and argument are functions of . Explicit expressions of these functions are given, and an approximation as is proved for the initial Painleve function outside a small neighborhood of its lattice of poles.
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