Formation of Saturated Solitons in a Nonlinear Dispersive System with Instability and Dissipation

A simple one-dimensional nonlinear equation including effects of instability, dissipation, and dispersion is examined numerically. It is observed that for the strongly dispersive case the temporal evolution is characterized by formation of a row of solitary pulses of equal equilibrium amplitudes. The width of each pulse is determined by the relative importance of the growing and the damping effects. The equilibrium amplitude increases as the dispersive effect increases.