Forces on Solitons in Finite, Nonlinear, Planar Waveguides

The forces acting on and the energies of solitons governed by the nonlinear Schr\"odinger equation in finite, planar waveguides with periodic and with homogeneous Dirichlet, Neumann and Robin boundary conditions are determined by means of a quantum analogy. It is shown that these densities have S-shape profiles and increase as the hardness of the boundary conditions is increased.