Velocity–amplitude relationships and polarizations in families of MHD solitary waves

Abstract

Plausible observations of MHD solitons by means of the Cluster system have recently been reported. The present paper addresses the theory of stationary wave forms obtained from MHD-type equations extended with Hall dispersion. Two aspects will be discussed: (i) the solitary wave solutions come in families, characterized by their velocity–amplitude relationship. The metamorphosis of these relationships will be described, starting with their form for small amplitude models (the KdV equation, the MKdV equation, the DNLS equation, and the triple-degenerate DNLS model), going through the cold plasma model, warm plasma scalar pressure model, and concluding with studies of models with anisotropic pressure. (ii) The predicted wave forms have a series of robust signatures well fitted for experimental tests. These include the polarization of the magnetic field through the structures (i.e., the magnetic hodograph), the relation between magnetic pressure and density perturbation, and the relation between the pressure components in the anisotropic models. These are also characterized in various families and models.