Dynamics of vortex structure formation during the evolution of modulation instability of dark solitons

The nonlinear stage of modulation instability of dark solitons is studied analytically and numerically. We propose an asymptotic description of the dynamics of these solitons in terms of their local velocity and the curvature of the lines at which solitons are concentrated. The features of the destruction of dark solitons (in particular, the formation of vortex structures from them) are analyzed.