The long time behavior of a finite amplitude shear Alfven wave in a warm plasma

The long time behavior of a monochromatic, finite amplitude shear Alfven wave is studied by means of the Krylov-Bogoliubov-Mitropolsky perturbation technique. The plasma model is assumed to be described by the linearly non-dispersive, ideal magnetohydro-dynamic equations. Non-linear coupling between the Alfven pump wave and a free sound wave gives rise to forced magnetic sidebands. It is shown that the Alfven pump wave as well as the magnetic sidebands steepen up in the long time scale. (author)