Darker-than-black solitons: Dark solitons with total phase shift greater than π

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Abstract
We discuss the stationary- and collisional-phase properties of dark optical solitons in a saturable nonlinear medium. Both the special case of an analytically solvable model of a saturable nonlinearity and other similar nonlinearities are considered. It is shown analytically that for a saturable nonlinearity the total phase shift across a single soliton may be much larger than π which is the maximum value in a Kerr medium and corresponds to a black soliton. Furthermore, for a given phase shift larger than π we find analytically that there exists two soliton solutions with different contrast. It is demonstrated numerically that these dark solitons which have an extraordinarily large total phase shift, propagate stably, and survive after collisions, maintaining almost the same large value of the phase shift. Additionally, we show that the stability criterion introduced earlier for multiple dark solitons is not sufficiently general and is effective only for some types of nonlinearity.