Acceleration of Alfven solitons

We study the dynamics of solitons perturbed by an external harmonic driver. These are described by a derivative nonlinear Schroedinger equation (DNLSE) which we solve by pseudo-spectral simulations over a 1024 point grid. Under the action of the perturbation, low-amplitude non-linearly interacting wave modes develop, which eventually degenerate into chaotic oscillations characterized by a positive maximum Lyapunov exponent and a large dimension. After this stage (which lasts about 10 driver's periods), an initially injected soliton (the initial condition) sets down to a train of pulse-shaped structures. These pulses have all the same speed and move in the same direction of the original soliton, retaining its polarization. However, the number of pulses in the numerical box and the time interval between them point out a translation speed which is about 4 times the one of the original soliton; the amplitude and width of the pulses are respectively about 2 and 1/4 times the ones of the original soliton. This suggests that the observed structure is itself a soliton which in fact solves the DNLSE. In other words, it appears as if the DNLSE nonlinearly stored the energy intake out of the driver into more energetic, faster and narrower solitons, a phenomenon we refer to as soliton acceleration. In the meanwhile, the above reported chaotic oscillations have entered an energy-cascade regime, and they have generated a low-level turbulent background in which the solitary structure is embedded. These features are spectrally 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. (orig.)