Saturday, August 12

MS45
Periodic Waves and Their Stability

1:30 PM-3:30 PM
Koali (Salon 5)

Nonlinear evolutionary PDEs often admit periodic patterns in the form of travelling wave solutions. The search for such solutions, the analysis of their stability properties, and the role they play in understanding the full range of dynamical behavior in solutions of the original evolutionary system are all challenging and important questions. In particular, the analysis of both the stability and bifurcation of periodic waves presents a number of difficulties that are not present with other types of solutions such as fronts and solitary waves. The speakers in this session will focus on recent advances on these issues in both a general context, and also, in several important applications, including reaction-diffusion models in biology and chemistry.

1:30-1:55 Stability of Wavetrains with Large Spatial Period

Arnd Scheel, Frei Universität Berlin, Germany

2:00-2:25 Stability of Periodic Solutions of the Gray-Scott Equations

Edgardo Eszter, University of Michigan, Ann Arbor, USA

2:30-2:55 Complex Spatio-temporal Patterns in Predator-Prey Interactions

Robert A. Gardner, Organizer

3:00-3:25 Modulating Multi-pulse Solutions for Dissipative Systems

Hannes Uecker, Universität Bayreuth, Germany