An analysis of unidimensional soliton gas models of magnetohydrodynamic turbulence in the solar wind

Two statistical models of Alfven solitons are compared whose evolution is described by the one-dimensional derivative nonlinear Schroedinger (DNLS) equation, contrasting their predictions with solar wind observations. Both distribution functions give the same mean number of solitons. One of the distribution functions follows an exponential law with soliton energy and the other follows a power law; the latter gives better results than the former. Within these models, the variation of the observed spectra with the heliocentric distance can be explained. This variation is related to the radial dependence of the mean level of modulation instability in the medium. 47 refs.