The Korteweg--de Vries Equation and an Introduction to the Theory of Integrable Systems -- Dmitry Zakharov <p>

The Korteweg--de Vries equation is a prototypical example of an  integrable system, a nonlinear PDE which can be exactly solved for a  wide class of initial data. I will give a brief 
overview of  Hamiltonian mechanics and explain the concept of an integral of  motion. I will then describe the Korteweg--de Vries equation, which is  an example of a system with an infinite 
number of integrals of motion.