Exact Solutions to Non-Linear Symmetron Theory: One and Two Mirror
  Systems
  We derive the exact analytical solutions to the symmetron field theory
equations in the presence of a one or two mirror system. The one dimensional
equations of motion are integrated exactly for both systems and their solutions
can be expressed in terms of Jacobi elliptic functions. Surprisingly, in the
case of two parallel mirrors the equations of motion generically provide not a
unique solution but a discrete set of solutions with increasing number of nodes
and energies. The solutions obtained herein can be applied to qBOUNCE
experiments, neutron interferometry and for the calculation of the symmetron
field induced "Casimir force" in the CANNEX experiment.
