We use Hamiltonian ray tracing and phase-space representation to describe the
propagation of a single spatial soliton and soliton collisions in a Kerr
nonlinear medium. Hamiltonian ray tracing is applied using the iterative
nonlinear beam propagation method, which allows taking both wave effects and
Kerr nonlinearity into consideration. Energy evolution within a single spatial
soliton and the exchange of energy when two solitons collide are interpreted
intuitively by ray trajectories and geometrical shearing of the Wigner
distribution functions.Comment: 12 pages, 5 figure
