题目: Analytic approach to the KdV equation

主讲人：张成（上海大学）

时间：

6月21日 19:00-21:30

6月22日 14:30-17:00

7月5日   14:30-17:00

7月6日   14:30-17:00

地点：东区管理科研楼1308教室 

课程内容:

1. Hierarchy of the KdV equations

2. Inverse scattering transform for KdV and soliton solutions

3. Periodic problems for KdV and finite-gap integration

4. Algebraic-geometric solutions

摘要: In this mini-lecture, I will present analytic approaches for solving initial-value problems for the KdV equation. The notion of Lax pair will first be introduced (through the so-called Miura transformation), and the central object is the so-called Schrodinger operator. This allows for constructing the hierarchy of KdV equations, and most of analysis will be based on the Schrodinger operator.Then the inverse scattering transform and finite-gap integration method will be discussed in details, aiming to solve KdV for various types of IVPs. If time allows, I will briefly present the so-called algebraic-geometric solutions for KdV following ideas of Krichever.