A polarization change of localized and finite-amplitude Alfv\'en waves is found by use of both MHD theory and numerical simulation. One of the transverse components of the circularly polarized Alfv\'en wave is stable as it propagates, but the other component is unstable under both self-focusing and diffraction effects. Consequently, the wave changes its polarization from circular to linear.
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M. Hoshino (1987) studied this question.
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