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Compressive solitary waves in compacting media. (English) Zbl 0754.76085
Summary: Compressive solitary wave solutions of a nonlinear partial differential equation proposed by D. R. Scott and D. J. Stevenson [Geophys. Res. Lett. 11, No. 11, 1161-1164 (1984)] to describe the one- dimensional migration of melt through the Earth’s mantle are investigated. It is shown that the dimensionless wave speed is equal to the exponent $$n$$ in the power law relating the permeability of the medium of the voidage. Three compressive solitary wave solutions are derived. The three solutions are algebraic solitary waves.

##### MSC:
 76V05 Reaction effects in flows 35Q51 Soliton equations 86A60 Geological problems
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