Approximate solutions for magmon propagation from a reservoir

Abstract

A 1D partial differential equation (pde) describing the flow of magma in the Earth's mantle is considered, this equation allowing for compaction and distension of the surrounding matrix due to the magma. The equation has periodic travelling wave solutions, one limit of which is a solitary wave, called a magmon. Modulation equations for the magma equation are derived and are found to be either hyperbolic or of mixed hyperbolic/elliptic type, depending on the specific values of the wave number, mean height and amplitude of the underlying modulated wave. The periodic wave train is stable in the hyperbolic case and unstable in the mixed case. Solutions of the modulation equations are found for a..