We investigate the propagation of a partially coherent beam in a nonlinear medium with logarithmic nonlinearity. We show that all information about the properties of the beam, as well as the condition for formation of incoherent solitons, can be obtained from the evolution equation for the mutual coherence function. The key parameter is the detuning $\Delta$ between the effective diffraction radius and the strength of the nonlinearity. Stationary partially coherent solitons exist when $\Delta =0\mathrm{}$ and the nonlinearity exactly compensates for the spreading due to both diffraction and incoherence. For nonzero detunings the solitons are oscillating in nature, and we find approximate solutions in terms of elliptic functions. Our results establish an elegant equivalence among several different approaches to partially coherent beams in nonlinear media.

• Received 13 April 1999

DOI:https://doi.org/10.1103/PhysRevE.61.3122