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Analytical Methods for Integrable Systems
可积性系统的解析解法

Abstract: (摘要) This mini-course consists of two parts. The first part is a rapid treatment of Riemann surfaces (or algebraic curves) and holomorphic vector bundles on them. The second part is on solving the Lax equations with spectral parameter. We will see how certain nonlinear PDE becomes equivalent to a linear flow on the Jacobian of the associated spectral curve. The theory will be applied to solve some classical integrable systems.

Prerequisite: 大三以上，学过复分析和微分方程。

Main References: (主要参考书)

1. Lecture notes by Hitchin: Riemann Surfaces and Integrable Systems

2. Textbook by 3 physicists Olivier Babelon, Michel Talon and Denis Bernard: Introduction of classical integrable systems

课程时刻表
 简介；黎曼面
 线丛和层论
 向量丛
 矩阵多项式和Lax方程
 线性化定理