Modulational instability of bright solitary waves in incoherently coupled nonlinear Schrödinger equations

We present a detailed analysis of the modulational instability (MI) of ground-state bright solitary solutions of two incoherently coupled nonlinear Schrödinger equations. Varying the relative strength of cross-phase and self-phase effects we show the existence and origin of four branches of MI of the two-wave solitary solutions. We give a physical interpretation of our results in terms of the group-velocity-dispersion- (GVD-) induced polarization dynamics of spatial solitary waves. In particular, we show that in media with normal GVD spatial symmetry breaking changes to polarization symmetry breaking when the relative strength of the cross-phase modulation exceeds a certain threshold value. The analytical and numerical stability analyses are fully supported by an extensive series of numerical simulations of the full model.