• Alfredo Wetzel
  • March 7, 2 PM
  • 2866 East Hall

Roughly speaking, in classical mechanics a dynamical system with enough constants of motion may, at least in principle, be solved in closed form. Such systems are called completely integrable and needless to say abound in physics.

In this talk, I will describe what is meant by an infinite-dimensional completely integrable system using some well known results of the Korteweg-de Vries (KdV) equation. In particular, I will begin by discussing some of the basic structure of finite dimensional Hamiltonian systems and explain more carefully what complete integrability means in this context. I will continue by showing how the KdV equation itself can be written in Hamiltonian form and discuss why this is significant for both the mathematics and physics of the problem. Even though many of these terms may sound technical, the talk is intended to be intuitive and accessible to everyone.