Instability-induced dynamics of dark solitons

Nonlinear theory describing the instability-induced dynamics of dark solitons in the generalized nonlinear Schr\"odinger equation is presented. Equations for the evolution of an unstable dark soliton, including its transformation into a stable soliton, are derived using a multiscale asymptotic technique valid near the soliton instability threshold. Results of the asymptotic theory are applied to analyze dark solitons in physically important models of optical nonlinearities, including competing, saturable, and transiting nonlinearities. It is shown that in all these models dark solitons may become unstable, and two general (bounded and unbounded) scenarios of the instability development are investigated analytically. Results of direct numerical simulations of the generalized nonlinear Schr\"odinger equation are also presented, which confirm predictions of the analytical approach and display main features of the instability-induced dynamics of dark solitons beyond the applicability limits of the multiscale asymptotic theory. {} 1996 The American Physical Society.