  We consider domain walls (DW's) between single-mode and bimodal states that
occur in coupled nonlinear diffusion (NLD), real Ginzburg-Landau (RGL), and
complex Ginzburg-Landau (CGL) equations with a spatially dependent coupling
coefficient. Group-velocity terms are added to the NLD and RGL equations, which
breaks the variational structure of these models. In the simplest case of two
coupled NLD equations, we reduce the description of stationary configurations
to a single second-order ordinary differential equation. We demonstrate
analytically that a necessary condition for existence of a stationary DW is
that the group-velocity must be below a certain threshold value. Above this
threshold, dynamical behavior sets in, which we consider in detail. In the CGL
equations, the DW may generate spatio-temporal chaos, depending on the
nonlinear dispersion.
