ABSTRACT
We have studied in chapters 4-6 the properties of numerous waves and instabilities by assuming a harmonic wave solution that is proportional to exp(−iωt + ik · r). This means that we have dealt with a wide variety of small-amplitude waves which are driven by linear and nonlinear mechanisms. There are numerous processes via which unstable modes can saturate and attain large amplitudes. When the amplitudes of the waves are sufficiently large, nonlinearities cannot be ignored. The nonlinearities come from the harmonic generation involving fluid advection, the nonlinear Lorentz force, trapping of particles in the wave potential, ponderomotive force, etc. The nonlinearities in plasmas contribute to the localization of waves, leading to different types of interesting coherent structures (namely solitary structures, shock waves, vortices, etc) which are important from both theoretical and experimental points of view.
