Abstract

We will address the following questions: What does it mean to be a 'dispersive' PDE? How to solve a linear Schrödinger equation? What about the nonlinear case? What’s Terry got to do with it? I will provide a basic introduction to the theory of linear Schrödinger equation, while highlighting differences to other basic PDE’s, such as heat equation. The goal will be to solve a nonlinear Schrödinger equation using a fixed-point argument. Along the way, the only tool we will (heavily) use is the Fourier transform.