MS31 ~ Tuesday, May 23, 1995 ~ 10:00 AM

Rigorous Theory of Weakly Nonlinear, Extended Systems

Spatially extended systems are ubiquitous in applications and present fascinating mathematical problems. Many phenomena occur in such systems that are impossible for finite dimensional dynamical systems _ for example, one sometimes finds that Hamiltonian systems are asymptotically stable in this context. The speakers will explore several avenues which have recently expanded the understanding of such systems, and which point out both their similarities to, and differences from, finite dimensional systems. In particular, they will examine the existence of normal forms for such systems, the applications of invariant manifold theorems in this context, justification of the frequently used modulation equations, and recent advances in the understanding of stability of travelling waves in such systems.

Organizer: Eugene Wayne, Pennsylvania State University

Stability and Instability of Solitary Waves
Robert Pego, University of Maryland, College Park
Modulation Equations as Reduction Method-Validity and Limitation
Guido Schneider, UniversitĄt Hannover, Germany
Normal Forms for Partial Differential Equations
Jalal Shatah, Courant Institute of Mathematical Sciences, New York University
Invariant Manifold Theorems for Partial Differential Equations on Unbounded Spatial Domains
Eugene Wayne, Organizer