• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to project page

2022 Fiscal Year Final Research Report

The Stokes phenomenon on linear or nonlinear, differential and differential equations

Research Project

  • PDF
Project/Area Number 19K03566
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionThe University of Tokushima

Principal Investigator

OHYAMA Yousuke  徳島大学, 大学院社会産業理工学研究部(理工学域), 教授 (10221839)

Project Period (FY) 2019-04-01 – 2023-03-31
Keywordsストークス現象 / 接続問題 / 超幾何方程式 / パンルヴェ方程式
Outline of Final Research Achievements

The problem of determining the relation between solutions of differential or difference equations at different points is called a connection problem. Moreover, solutions in the neighborhood of singular points are expressed by divergent power series, and the phenomenon where the true solution differs in different regions is called the Stokes phenomenon. We solve connection problems and the Stokes phenomena in the case of higher order q-hypergeometric difference equations and some q-Painleve equations. In particular, we discover that the space of connection for the q-Painleve VI equation, known as the character manifold, becomes the Segre surfaces, i.e., fourth-order Del Pezzo surfaces.

Free Research Field

古典解析学

Academic Significance and Societal Importance of the Research Achievements

微分方程式・差分方程式の接続問題は数理科学の基本的な問題の一つです。またストークス現象も19世紀より知られており、収束しない発散級数を意味付けすることは新しい数学の源泉の一つです。q-差分方程式の場合のストークス現象の研究によって場の量子論など現代的な数理科学への応用が見込まれます。また、q-パンルヴェ方程式の大域解析のためにもq-ストークス問題を解くことが必要になりますが、q-超幾何方程式のストークス現象を用いて、q-パンルヴェ方程式の指標多様体の構造が明確になり、さらなら発展が期待できます。

URL: 

Published: 2024-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi