Waves induced by heterogeneity in oscillatory media

Abstract

Abstract Various behaviours of nonlinear wave propagation and competition have been discussed and investigated extensively and meticulously, especially when the media are homogeneous. However, corresponding studies in heterogeneous media are much scarcer. In this paper, spontaneously generated waves from one-dimensional heterogeneous oscillatory media, modelled by complex Ginzburg–Landau equations with spatially varied controlling parameters, are investigated. An unexpected homogeneous wave train clearly emerges under certain conditions. With the theory of interface-selected waves, we can theoretically predict the frequencies and wavenumbers under several conditions. This kind of wave train can be found in a wide region of parameter space. These phenomena are robust when parameters are varied nonlinearly or linearly with fluctuation. Moreover, this kind of homogeneous wave plays an important role in wave competition and affects wave propagation in spatially heterogeneous nonlinear systems, which will bring new applications of heterogeneity and provide new ideas for wave control.