MODULATIONS OF SLOW SAUSAGE SURFACE-WAVES TRAVELING ALONG A MAGNETIZED SLAB

In this paper we consider a set of nonlinear MHD equations that admits in a linear approximation a solution in the form of a slow sausage su rface wave travelling along an isolated magnetic slab. For a wave of s mall but finite amplitude, we investigate how a slowly varying amplitu de is modulated by nonlinear self-interactions. A stretching transform ation shows that, at the lowest order of an asymptotic expansion, the original set of equations with appropriate boundary conditions (free i nterfaces) can be reduced to the cubic nonlinear Schrodinger equation, which determines the amplitude modulation. We study analytically and numerically the evolution of impulsively generated waves, showing a tr ansition of the initial states into a train of solitons and periodic w aves. The possibility of the existence of solitary waves in the solar atmosphere is also briefly discussed.