ACCELERATION OF ALFVEN SOLITONS

We study the dynamics of solitons perturbed by an external harmonic dr iver. These are described by a Derivative Nonlinear Schrodinger Equati on (DNLSE) which we solve by pseudo-spectral simulations over a 1024 p oint grid. Under the action of the perturbation, low-amplitude non-lin early interacting wave modes develop, which eventually degenerate into chaotic oscillations characterized by a positive maximum Lyapunov exp onent and a large dimension. After this stage (which lasts about 10 dr iver's periods), an initially injected soliton (the initial condition) sets down to a train of pulse-shaped structures. These pulses have al l the same speed and move in the same direction of the original solito n, retaining its polarization. However, the number of pulses in the nu merical box and the time interval between them point out a translation speed which is about 4 times the one of the original soliton; the amp litude and width of the pulses are respectively about 2 and 1/4 times the ones of the original soliton. This suggests that the observed stru cture is itself a soliton which in fact solves the DNLSE. In other wor ds, it appears as if the DNLSE nonlinearly ''stored'' the energy intak e out of the driver into more energetic, faster and narrower solitons, a phenomenon we refer to as ''soliton acceleration''. In the meanwhil e, the above reported chaotic oscillations have entered an energy-casc ade regime, and they have generated a low-level turbulent background i n which the solitary structure is embedded. These features are spectra lly analyzed to produce power-law wave-number and frequency spectra An inertial range exists where the spectral indexes are about -1.45 and -1.5 for the wave-number and the frequency spectrum respectively.