Multiscale methods for Hamiltonian systems

Konserwatorium wydziałowe. Abstract. Many physical system involve several spatial or temporal scales. Often it is desirable to find effective macroscopic models that describe the essential features without resolving the small scales. In particular we discuss the passage from discrete lattice systems to continuous models. We discuss the well-known fact that macroscopic pulses of microscopically periodic patterns are governed by the nonlinear Schr�dinger equation. However, we use a new approach based on the Hamiltonian and Lagrangian structures as well as the symmetry invariants.