### Thursday, May 22

10:00 AM-12:00 PM
*Magpie A & B - Level B*

## MS46

Energy Transfer in Nonlinear Partial Differential Equations

In nonlinear and nonintegrable partial differential equations (PDEs) modeling physical systems, important phenomena are often understandable in terms of energy transfer among natural modes of the system. Such descriptions can be, for example, in terms of (nonlinear) bound state and radiation modes, or small scale and long scale structures. In this minisymposium some conservative and dissipative dynamical systems will be considered and analyzed from this perspective. Examples of phenomena to be examined are asymptotic stability, metastability, radiation damping, singularity formation in Hamiltonian systems, and turbulence in random and dissipatively perturbed Hamiltonian systems. The equations considered are nonlinear wave and Schrödinger equations and their perturbations. The methods used are quite broad and involve, for example, classical PDE and asymptotic methods, invariant manifolds, scattering theory and stochastic analysis. The purpose of this minisymposium is to present in a single forum recent evelopments on the question of energy transfer in nonlinear and nonintegrable PDEs.

**Organizer: Michael I. Weinstein**

*University of Michigan , Ann Arbor*

**10:00 Self-Focusing of the Nonlinear Schrödinger Equation and Its Behavior Under Small Perturbation**
- George C. Papanicolaou, Stanford University
**10:30 Invariant Manifolds for a Class of Dispersive, Hamiltonian, Partial Differential Equations**
- Claude-Alain Pillet, Universite de Geneve, Switzerland; and
*Clarence Eugene Wayne*, Pennsylvania State University
**11:00 On Oscillations of Solutions of Randomly Forced-Damped NLS Equations**
- Sergei B. Kuksin, Steklov Mathematical Institute, Russia
**11:30 Resonances and Radiation Damping in Conservative Nonlinear Waves**
- Michael I. Weinstein, Organizer

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*TMP, 4/4/97*