The evolution of nonlinear Alfven waves subject to growth and damping

The effects of wave amplification (by streaming particle distributions) and damping (by ion-cyclotron resonance absorption) on the nonlinear evolution of Alfven waves are investigated theoretically. The results of numerical simulations based on the derivative-Schroedinger-equation model of Spangler and Sheerin (1983 and 1985) are presented graphically and characterized in detail, with an emphasis on astrophysical applications. Three phases of wave-packet evolution (linear, nonlinear-saturation, and postsaturation quasi-steady) are identified, and nonlinearity is found to transfer wave energy from growing or amplified wavenumbers to wavenumbers affected by damping. It is pointed out that although there are similarities between the solitonlike pulses predicted by the simulations and short-wavelength shocklet structures observed in the earth bow shock, the model does not explain why low-frequency waves stop growing in the vicinity of the bow shock.