Traveling hole solutions of the complex Ginzburg–Landau equation: a review

This paper reviews recent works on localized solutions of the one-dimensional complex Ginzburg–Landau (CGL) equation known as traveling holes. Such coherent structures seem to play an important role in the disordered dynamics displayed by CGL at a finite distance past the Benjamin–Feir instability threshold. We discuss these objects in the broader context of weak turbulence and summarize some of their properties.