An important step in understanding the solution of systems of nonlinear partial differential equations is the analysis of relative equilibria like traveling waves (one spatial dimension) or rotating waves (two spatial dimensions). In this talk I will mainly focus on how to capture traveling waves numerically by using the freezing method. Generalizations to more general symmetries will also be considered. As an example class I look at the case of semilinear, non-strictly hyperbolic reaction diffusion systems. These naturally arise, if instead of Fouriers law one uses the Cattaneo-Maxwell law as a constitutive relation for the flux of reactants.