The effects of generalized dispersion on dissipative dynamical systems

We study the effects of dispersion on the Kuramoto-Sivashinsky (KS) equation. In the physical problem considered, there is a full dispersion relation corresponding to a pseudo-differential linear operator added to the KS equation. The long wave limit of this term localizes to a KortwegdeVries dispersion and we present results from extensive numerical experiments that compare the long time evolution of the global and local systems. It is found that solutions are almost identical in both fixed point (steady traveling waves) and time periodic attractors.