The Cauchy problem for the quasilinear Schrodinger equatio

TL;DR

This paper provides lecture notes on the Cauchy problem for the quasilinear Schrödinger equation, summarizing joint work by Kenig, Ponce, and Vega, including problem sets and solutions for a summer course.

Contribution

It compiles and explains key results on the well-posedness of the quasilinear Schrödinger equation based on the authors' joint research.

Findings

Summarizes methods for solving the Cauchy problem

Includes problem sets with solutions for educational purposes

Highlights advances in understanding quasilinear Schrödinger equations

Abstract

These are lectures notes for a 6 hour course given at PCMI, Park City, Utah, in the summer of 2003. The notes are based on a series of joint works of Kenig-Ponce-Vega. Each lecture had problems assigned with it. The lecture notes were prepared with the help of Justin Holmer. Justin Holmer also provided solutions to the problems, in an appendix to the notes.