Interface-selected waves and their influence on wave competition

In this paper we study nonlinear oscillatory systems consisting of two media, one supporting forward propagating waves and the other inwardly propagating waves, separated by an interface. We find that the interface can select the type of wave. Under certain well-defined parameter condition, these waves propagate in two different media with the same frequency and same wave number; the interface of the two media is transparent to these waves. The frequency and wave number of these interface-selected waves (ISWs) are predicted explicitly. When parameters are varied from this parameter set, the wave numbers of the two domains become different, and the difference increases from zero continuously as the distance between the given parameters and this parameter set increases from zero. It is found that ISWs can play crucial roles in practical problems of wave competition, e.g., ISWs can suppress spirals and antispirals.