• Alfredo Wetzel
  • April 6, 1 PM
  • 3866 East Hall
Many of the PDEs that describe physical systems admit wave-like  
phenomena. However, most of us are used to hyperbolic systems, e.g.,  
the wave equation. In the case of waves in water, structural beams, or  
crystal optics to name a few, it is best to take a different approach  
of study since waves in these media can "disperse". That is, a  
coherent wave packet will spread out according to the different modes  
in the packet.

This presentation is intended to be a brief introduction to some of  
the basic theory of linear dispersive waves. In particular, I will  
present the concepts of phase and group velocity and how they arise  
from simple asymptotics and kinematic considerations. Also, I will  
talk about conservation laws that arise in the analysis of the wave  
number and energy propagation of dispersive waves. I will finish by  
showing how the theory applies to capillary and deep water waves and  
provide physical examples where this theory can be readily seen. This  
leads to some surprising results for those of us who are used to  
non-dispersive waves.