Long-Alfvén-wave trains in collisionless plasmas. II. A Landau-fluid approach

A Hall Landau-fluid model where the fluid hierarchy is closed by nonlocal dynamical equations for the heat fluxes is constructed, based on a weakly nonlinear description of long parallel Alfvén waves in a collisionless plasma. This model which is shown to accurately reproduce the above asymptotic regime, can be viewed as a first step towards the simulation of dispersive Alfvén wave turbulence with a realistic dissipation.