Cnoidal electron hole propagation: Trapping, the forgotten nonlinearity in plasma and fluid dynamics

In this review a plaidoyer is held for a specific form of nonlinearity, the trapping nonlinearity (TN), which arises due to a capture of particles and/or fluid elements in an excited coherent structure. This is of some importance since it appears that TN has not yet taken roots hitherto, neither in turbulence nor in anomalous transport models. The present state of knowledge about wave excitation, seen numerically and experimentally, especially at space craft, however, speaks a different language suggesting that current wave models are constructed too narrowly to reflect reality. The focus is on traveling cnoidal electron holes (CEHs) in electrostatically driven plasmas and the physical world associated with these. As a result a new wave concept emerges, in which the low amplitude dynamics is nonlinearly controlled by TN.