Incoherent spatial solitons in inertial nonlinear media

Spatial solitons represent an optical beam propagating in a nonlinear medium without changing its shape. Typically spatial solitons are created by self-trapping of the coherent optical beams, i.e. beams whose phase at any two points is fully correlated. Such beams differ significantly from those generated by an incoherent light source in which there is no correlation between light emitted from two different points. In effect, the phase across beam exhibits some level of randomness (partial correlation). A partially coherent beam spreads faster than the coherent beam of the same diameter. Additionally the intensity distribution of the partially coherent beam assumes time varying speckle structures making impossible self-focusing in typical instantaneous media. It has been shown recently, that the self-focusing of the partially coherent beam is still possible provided the nonlinear medium is inertial and responds on the time scale much longer than that of the fast phase variations