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.

中文翻译：

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振荡介质中由异质性引起的波

已经对非线性波传播和竞争的各种行为进行了广泛而细致的讨论和研究，尤其是在介质是均质的情况下。然而，对异质媒体的相应研究却少得多。在本文中，研究了由具有空间变化控制参数的复杂 Ginzburg-Landau 方程建模的一维异质振荡介质自发产生的波。在某些条件下，明显出现了意想不到的均匀波列。借助界面选择波理论，我们可以从理论上预测几种条件下的频率和波数。这种波列可以在广泛的参数空间区域中找到。当参数非线性或随波动线性变化时，这些现象是稳健的。而且，