NONLINEAR-WAVE PROPAGATION ALONG A MAGNETIC-FLUX TUBE

The weakly nonlinear wave propagation of a slow sausage surface wave t raveling along a magnetized slab with a thin nonuniform boundary layer is considered. The ideal incompressible MHD equations are used and th e nonlinearities are assumed to be due to second harmonic generation. A nonlinear dispersion relation and the related nonlinear Schrodinger equation is derived. The existence of a continuous thin interface lead s to sharply peaked field amplitudes due to resonant interaction with local Alfven waves. It is shown that the nonlinear effects from proces ses within the thin layer are much more important than those from the main slab. Furthermore, the nonlinear interaction with local Alfven wa ves yields a nonlinear damping rate of the wave that is much larger th an the linear damping rate when the transition layer is sufficiently t hin.