Variety of nonlinear wave-breaking

We discuss the formation of typical (structurally stable) singularities in nonlinear wave breaking in stable and unstable media. The wake wave-break due to the inhomogeneity of the Langmuir frequency is accompanied by electron injection into the acceleration phase. In a wake wave excited behind a finite width laser pulse, the wave-breaking mechanism involves the increase, with the distance behind the pulse, of the curvature of the wake front, followed by the self-intersection of the electron trajectories. In the long wavelength limit, the Weibel instability which leads to the generation of a strong magnetic field, the relativistic self focusing and the Rayleigh–Taylor instability of a thin plasma slab provide examples of a common behavior with the rarefaction wave-breaking in unstable media. We present a solution of the Cauchy problem that describes the evolution of nonlinear perturbations of the Rayleigh–Taylor instability in terms of analytical functions of a complex variable.