We investigate the stability of the one-dimensional solitary waves solutions of the equations proposed by McKenzie to model the ascent of melts in the Earth interior. We show that for small porosity and two-dimensional horizontal disturbances with long wavelength, these solitary waves are unstable. We also exhibit two- and three-dimensional solitary-wave solutions of the McKenzie equations.
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Barcilon et al. (1989) studied this question.
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