Confined states in phase dynamics: The influence of boundary conditions and transient behavior

Confined states in phase dynamics\char21{}the coexistence of states with different wavelengths\char21{}are further studied. In particular, a stable and accurate numerical code is developed to study the dynamic equation of motion for two sets of boundary conditions\char21{}a pinned phase and an unpinned phase. With a pinned phase, stable confined states are found to exist for a wide range of parameter values. With an unpinned phase, the localized states are at best neutrally stable. Also, analytic solutions are found for the stationary confined states.