Transverse modulational instability of partially incoherent soliton stripes

Based on the Wigner distribution approach, an analysis of the effect of partial incoherence on the transverse instability of soliton structures in nonlinear Kerr media is presented. It is explicitly shown, that for a Lorentzian incoherence spectrum the partial incoherence gives rise to a damping which counteracts, and tends to suppress, the transverse instability growth. However, the general picture is more complicated and it is shown that the effect of the partial incoherence depends crucially on the form of the incoherence spectrum. In fact, for spectra with finite rms-width, the partial incoherence may even increase both the growth rate and the range of unstable, transverse wave numbers.