An exact solution describing the self-similar dynamics of partially coherent light beams in nonlinear and noninstantaneous Kerr media is presented and analyzed. The description is based on the Wigner formalism for analyzing the propagation of partially coherent light. The solution for the Wigner distribution corresponds to a transverse beam intensity profile of a parabolic form, and the effects of the partial coherence on the beam dynamics are analyzed. The presence of partial coherence in the parabolic beam is shown to increase the diffraction effect, thus weakening the nonlinear self-focusing and increasing the defocusing rate. In the case of an almost coherent beam and a strongly nonlinear situation in a defocusing medium, the new solution is shown to reduce to a previously given parabolic similarity solution for coherent high intensity beam–pulse propagation.
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