  We present a model problem for benchmarking codes that investigate magma
migration in the Earth's interior. This system retains the essential features
of more sophisticated models, yet has the advantage of possessing solitary wave
solutions. The existence of such exact solutions to the nonlinear problem make
it an excellent benchmark problem for combinations of solver algorithms. In
this work, we explore a novel algorithm for computing high quality
approximations of the solitary waves and use them to benchmark a
semi-Lagrangian Crank-Nicholson scheme for a finite element discretization of
the time dependent problem.
