Nonlinear Partial Differential Equations, Birkhoff Normal Forms, and KAM Theory

The purpose of this talk is twofold. First, I want to give another example of how tools and techniques which are well proven in the world of finite dimensional dynamical systems may be applied in the world of infinite dimensional evolution equations. In this case the tool is the so-called Birkhoff normal form of Hamiltonian mechanics, which allows Hamiltonian systems near an equilibrium to be viewed as small perturbations of integrable systems. In the infinite dimensional world, such a normal form allows us to view certain nonlinear evolution equations not only as small perturbations of integrable partial differential equation, but also as small perturbations of infinite dimensional, integrable ordinary differential equations. In addition, the calculations involved are rather elementary. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.