Applied analysis by discrete integrable systems and discrete differential geometry

2014 Fiscal Year Final Research Report

• Project/Area Number: 23340037
• Research Category: Grant-in-Aid for Scientific Research (B)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: Kyushu University
• Principal Investigator: KAJIWARA Kenji 九州大学, マス・フォア・インダストリ研究所, 教授 (40268115)
• Co-Investigator(Kenkyū-buntansha): INOGUCHI Jun-ichi 山形大学, 理学部, 教授 (40309886) ; NAKAYASHIKI Atsushi 津田塾大学, 学芸学部, 教授 (10237456) ; MASUDA Tetsu 青山学院大学, 理工学部, 准教授 (00335457) ; OHTA Yasuhiro 神戸大学, 大学院理学研究科, 教授 (10213745)
• Co-Investigator(Renkei-kenkyūsha): MATSUURA Nozomu 福岡大学, 理学部, 助教 (00389339)
• Project Period (FY): 2011-04-01 – 2015-03-31
• Keywords: 離散可積分系 / 離散微分幾何 / 離散曲面・曲線論 / 離散正則函数 / τ函数 / ソリトン方程式 / パンルヴェ方程式 / 超幾何函数

Outline of Final Research Achievements

By applying the theory of discrete integrable systems, studies on good discretization of geometric objects such as curves and surfaces have been carried out. The main results are as follows: (1) Discrete curve theory. Development of deformation theory of plane and space discrete curves and construction of explicit formula in terms of the tau functions. (2) Theory of discrete analytic functions. Construction of explicit formula for the discrete power function in terms of hypergetomtric tau function of the Painleve VI equation and generalization. (3) As an application, systematic construction of stable and highly accurate numerical scheme for nonlinear wave phenomena in terms of self-adaptive moving mesh scheme based on discretization of the Euler-Lagrange transformation.

Free Research Field

可積分系，離散微分幾何