{"title":"A coalescent diagram of the Painlevé equations from the viewpoint of isomonodromic deformations","authors":"Y. Ohyama, S. Okumura","doi":"10.1088/0305-4470/39/39/S08","DOIUrl":null,"url":null,"abstract":"We revise Garnier–Okamoto's coalescent diagram of isomonodromic deformations and give a possible coalescent diagram from the viewpoint of isomonodromic deformations. We have ten types of isomonodromic deformations and two of them give the same type of Painlevé equation. We can naturally put the 34th Painlevé equation in our diagram, which corresponds to the Flaschka–Newell form of the second Painlevé equation.","PeriodicalId":87442,"journal":{"name":"Journal of physics A: Mathematical and general","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2006-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"67","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/S08","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 67
Abstract
We revise Garnier–Okamoto's coalescent diagram of isomonodromic deformations and give a possible coalescent diagram from the viewpoint of isomonodromic deformations. We have ten types of isomonodromic deformations and two of them give the same type of Painlevé equation. We can naturally put the 34th Painlevé equation in our diagram, which corresponds to the Flaschka–Newell form of the second Painlevé equation.