Unified model for partially coherent solitons in logarithmically nonlinearmedia

We investigate the propagation of a partially coherent beam in a nonlinear medium with logarithmic nonlinearity. We show that all information about th e properties of the beam, as well as the condition far formation of incoher ent solitons, can be obtained from the evolution equation for the mutual co herence function. The key parameter is the detuning Delta between the effec tive diffraction radius and the strength of the nonlinearity. Stationary pa rtially coherent solitons exist when Delta = 0 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 appr oximate solutions in terms of elliptic functions. Our results establish an elegant equivalence among several different approaches to partially coheren t beams in nonlinear media.