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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 ⌬ between the effective diffraction radius and the strength of the nonlinearity. Stationary partially coherent solitons exist when ⌬ϭ0 and thedoi:10.1103/physreve.61.3122 fatcat:mpsur662nfhqzoj7outjkttdlq