Invariant tori for Hamiltonian PDE
نویسنده
چکیده
Many of the central equations of mathematical physics, the nonlinear wave equation, the nonlinear Schrödinger equation, the Euler equations for free surfaces, can be posed as Hamiltonian systems with infinitely many degrees of freedom. In a neighborhood of an equilibrium, the linearized equations are those of a harmonic oscillator and thus solutions exhibit periodic and quasi-periodic motion. To construct solutions of the same nature for the nonlinear partial differential equations (PDE)s is a small divisor problem in general. This article gives an overview of some of the techniques and results of KAM-like methods for PDE, which have been developed to address the analysis of this problem.
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