  We review and compare different computational variational methods applied to
a system of fourth order equations that arises as a model of cylinder buckling.
We describe both the discretization and implementation, in particular how to
deal with a 1 dimensional null space. We show that we can construct many
different solutions from a complex energy surface. We examine numerically
convergence in the spatial discretization and in the domain size. Finally we
give a physical interpretation of some of the solutions found.
