Properties of generalized solitary melt waves in a compressible medium of variable viscosity
We study properties of generalized solitary melt waves in a compressible porous medium where viscosity is a strongly nonlinear function of melt concentration. The study involves numerical analysis and analytical methods. Time and space distributions of melt concentration are calculated assuming a variable viscosity and several initial conditions (for the initial melt concentration taken as a Gaussian curve, a piecewise constant function, or a constant). Numerical results explain the initiation and evolution of waves in buoyant melt. We analyze numerical solutions and two first integrals of the compaction equation and conclude that nonlinear waves of a new kind emerge in real media where viscosity is a strongly nonlinear function of melt concentration. These waves have high amplitudes and add vigor to melt migration.