Theory of spatial solitons

The basic theory of spatial solitons is presented with an emphasis upon analytical results. It is shown that both diffusive and saturated nonlinearities can be treated mathematically and that solitonlike solutions exist. Soliton interactions are investigated, and their properties are exposed with a variational method, leading to a particle representation. Examples concerning spatial solitons coupled by polarization or by being coupled in separate, identical, planar waveguides are discussed in detail. It is shown that an escape velocity exists and that below this velocity, spatial solitons engage in a periodic interaction, for which the period can be readily defined. The mathematical analysis is confirmed by a numerical simulation.