Numerical simulation of attraction of partially spatially incoherent dark solitons

We investigate numerically the interactions of partially spatially incoherent odd dark solitons in a de-focusing kerr nonlinear media based on the coherent density approach, and find that a pair of partially spatially incoherent dark solitons may be changed from repulsion to attraction with an appropriate incoherence parameter. Moreover, a pair of partially incoherent gray soliton may form under appropriate conditions. Some numerical examples are provided to illustrate their interaction behavior further.