パンルヴェ方程式上の代数解析 Algebraic Analysis on Painleve Equations

Ohyama, Yousuke

World Scientific Publishing Co Pte Ltd（2024/08発売）

• 製本 Hardcover:ハードカバー版／ページ数 350 p.
• 言語 ENG
• 商品コード 9789812561947
• DDC分類 515.352

基本説明

Serves as a guide to algebraic studies on the Painleve equations and as an introduction to non-specialists. The book aims to be self-contained by presenting complete proofs of the theorems.

Full Description

In the past three decades, studies on the Painleve equations have rapidly developed through the efforts of many researchers in various fields. The Painleve equations have numerous applications to differential geometry, probability theory, soliton theory, topological field theory, and others. In the past ten years, the Painleve equations have been studied not only by analytic methods, but also by algebraic methods, such as rational algebraic surfaces, differential Galois theory, the affine Weyl groups, and representation theory. This book serves as a guide to algebraic studies on the Painleve equations and as an introduction to non-specialists. The book aims to be self-contained by presenting complete proofs of the theorems.

Contents

Nonlinear Differential Equations with No Movable Singularities; Isomonodromy Deformations; Initial Value Spaces; B�cklund Transformations;  Functions and Bilinear Equations; Irreducibility; Special Solutions; Discrete Painleve Equations; NoumiYamada Systems (Dressing Chain).