The temporal evolution of weakly nonlinear, plane, linearly polarized Alfvén pulses in a cold, homogeneous plasma has been investigated in the paper On the evolution of a nonlinear Alfvén pulse by Verwichte, Nakariakov & Longbottom (1999). A static initial pulse-like disturbance in transverse velocity produces two Alfvén pulses that travel in opposite directions along the magnetic field. The ponderomotive force of the two pulses produces a static shock in longitudinal velocity at the starting position. The travelling pulses form a shock front which is governed by the scalar Cohen-Kulsrud equation. We have found a good agreement between the analytical solutions we derived and the results from a fully nonlinear numerical MHD code.
Verwichte, E., Nakariakov, V.M. and Longbottom, A.: 1999, On the evolution of a nonlinear Alfven pulse, J. Plasma Phys., 62, 219-232.
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