Speaker: Charlie Brummitt, UW Department of Physics
Abstract: A search for the simplest chaotic partial differential equation (PDE) concludes that the Kuramoto-Sivashinsky equation is likely the simplest chaotic PDE. We enumerate all of the equations with one quadratic or cubic nonlinearity that are "simpler" than the Kuramoto-Sivashinsky equation and test them for chaos, but none appear to be chaotic. Nevertheless, the search finds a strikingly simple PDE that is chaotic in the discrete limit of finitely many, coupled ordinary differential equations (ODEs). Analysis of this finite system indicates why the chaos vanishes in the limit of infinitely many ODEs.