Study on limit set of KdV flow

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400128
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kwansei Gakuin University
• Principal Investigator: Kotani Shinichi 関西学院大学, 特定プロジェクト研究センター, 客員研究員 (10025463)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: シュレーデインガー作用素 / KdV方程式 / スペクトル / 力学系 / Toeplitz作用素 / Weyl関数

Outline of Final Research Achievements

Since the discovery of the deep connection between the KdＶ equation describing the dynamics of shallow water wave and the spectrum (eigenvalue) of 1d Schroedinger operator, the KdV equation has been studied in algebra, analysis and geometry as a typical completely integrable system. In this program we take a look of algebraic Sato's theory from the point of spectral theory of Schroedinger operators, and try to construct a solution to the KdV equation starting from a general initial data. To this end we could succeed to obtain an expression of the tau-function by the Weyl function for 1d Schroedinger operator. The tau-function is the key object in Sato's theory. This expression made it possible to give a general solution to the KdV equation.

Free Research Field

スペクトル理論，確率論