MS41 ~ Wednesday, May 24, 1995 ~ 10:00 AM

Applications of Dynamical Systems Methods to Nonlinear Waves

The construction of standing and travelling wave solutions of nonlinear pde together with a description of their stability properties, is an important means of obtaining insight into the qualitative behavior of general solutions. Wave solutions provide a natural connection between nonlinear pde and dynamical systems theory, and techniques from the latter area such as invariant manifold theory and topological methods have provided a powerful set of techniques for locating waves of various types, such as homoclinic, heteroclinic, and periodic waves, and also, for assessing their stability properties. This session explores the application of dynamical systems methods to waves solutions arising in several applications, including fluids, MHD, and the Ginzburg-Landau equations.

Organizers: Christopher K.R.T. Jones, Brown University and Robert A. Gardner, University of Massachusetts, Amherst

Instability of Travelling Wave Solutions of the Generalized Burgers-KdV Equations
Robert A. Gardner, University of Massachusetts, Amherst
Spatial Dynamics of Time Periodic Solutions for the Ginzburg-Landau Equation
T. Kapitula, University of Utah
Viscous Profiles for Magnetohydrodynamic Shock Waves
P. Szmolyan, Technische UniverstĄt Wien, Austria
Stability and Instability of Nonlinear Waves in Fluids and Lattices
Michael I. Weinstein, University of Michigan, Ann Arbor