| 书目名称 | Padé Methods for Painlevé Equations |
| 编辑 | Hidehito Nagao,Yasuhiko Yamada |
| 视频video | |
| 概述 | Presents an elemental method, assuming only standard linear algebra and complex analysis.Allows target equations such as Painlevé and Garnier systems to arise naturally through suitable Padé problems. |
| 丛书名称 | SpringerBriefs in Mathematical Physics |
| 图书封面 |  |
| 描述 | The isomonodromic deformation equations such as the Painlevé and Garnier systems are an important class of nonlinear differential equations in mathematics and mathematical physics. For discrete analogs of these equations in particular, much progress has been made in recent decades. Various approaches to such isomonodromic equations are known: the Painlevé test/Painlevé property, reduction of integrable hierarchy, the Lax formulation, algebro-geometric methods, and others. Among them, the Padé method explained in this book provides a simple approach to those equations in both continuous and discrete cases..For a given function .f.(.x.), the Padé approximation/interpolation supplies the rational functions .P.(.x.), .Q.(.x.) as approximants such as .f.(.x.)~.P.(.x.)/.Q.(.x.). The basic idea of the Padé method is to consider the linear differential (or difference) equations satisfied by .P.(.x.) and .f.(.x.).Q.(.x.). In choosing the suitable approximation problem, the linear differential equations give the Lax pair for some isomonodromic equations. Although this relation between the isomonodromic equations and Padé approximations has been known classically, a systematic study including |
| 出版日期 | Book 2021 |
| 关键词 | Padé approximation/interpolation; (Discrete) Painlvé and Garnier equations; Isomonodromic system, Lax |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-981-16-2998-3 |
| isbn_softcover | 978-981-16-2997-6 |
| isbn_ebook | 978-981-16-2998-3Series ISSN 2197-1757 Series E-ISSN 2197-1765 |
| issn_series | 2197-1757 |
| copyright | Springer Nature Singapore Pte Ltd. 2021 |
发表于 2025-3-21 18:02:29
