Theory of Incoherent Dark Solitons

We formulate the theory of incoherent dark spatial solitons in noninstantaneous self-defocusing nonlinear media. We find that the basic modal constituents of these incoherent dark soliton entities are radiation modes as well as bound states. Our results explain for the first time why incoherent dark solitons are in fact gray and why a transverse $\pi$-phase flip can facilitate their observation.