Instantaneous nonlinearities cannot trap an incoherent beam and form a soliton out
of it. If an incoherent beam is launched into a self-focusing nonlinear medium that re-
sponds almost instantaneously (e.g., a Kerr medium), each speckle forms a self-induced
waveguide that captures a small fraction of the beam. These tiny induced waveguides
intersect and cross each other in a random manner during beam propagation. The net
effect is that the beam breaks up into small fragments, and self-trapping of the beam
envelope does not occur. Thus, only a slow-responding nonlinear medium can support
incoherent solitons. ...
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