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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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