Nonlinear semiconductor transport simulations based on the WIAS-TeSCA code are presented. Various regimes of lowtemperature breakdown and current filamentation in n-GaAs are investigated using a drift-diffusion model with nonlinear generation-recombination kinetics. Nonlinear charge density waves are found in two-dimensional simulations of a point contact geometry with and without an additional perpendicular magnetic field. The numerical simulations of the nonlinear spatio-temporal dynamics are complemented by a linear stability analysis which reveals the possibility of undamped longitudinal fluctuations in the filamentary regime.