0Introduction

II Integrable Systems



0 Introduction
What is an integrable system? Unfortunately, an integrable system is a some-
thing mathematicians have not yet managed to define properly. Intuitively, an
integrable system is a differential equation we can “integrate up” directly. While
in theory, integrable systems should be very rare, it happens that in nature, a
lot of systems happen to be integrable. By exploiting the fact that they are
integrable, we can solve them much more easily.