STABILITY OF TRAVELING WAVES FOR A CONSERVED FIELD

The stability of traveling waves is investigated for a model describin g the post threshold behavior beyond oscillatory instabilities for a c lass of systems with a conserved order parameter. Oscillatory instabil ities and their post threshold behavior in systems with unconserved or der parameters have been a central topic of nonlinear science during t he recent decade. The most famous equation in this context is the Ginz burg-Landau equation with complex coefficients. Here I discuss a strai ght forward generalization of this Ginzburg-Landau equation which cove rs also spinodal decomposition and the crossover to an oscillatory ins tability for a globally conserved order parameter. Especially, the mod ification of the border to spatiotemporal chaos is considered, which i s described by the so-called Benjamin-Feir resonance.