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We describe a general N-solitonic solution of the focusing NLSE in thepresence of a condensate by using the dressing method. We give the explicitform of one- and two- solitonic solutions and study them in detail. Wedistinguish a special class of solutions that we call regular solitonicsolutions. Regular solitonic solutions do not disturb phases of the condensateat infinity by coordinate. All of them can be treated as localizedperturbations of the condensate. We find a broad class of superregularsolitonic solutions which are small perturbations at certain a moment of time.Superregular solitonic solutions are generated by pairs of poles located onopposite sides of the cut. They describe the nonlinear stage of the modulationinstability of the condensate and play an important role in the theory of freakwaves.

Superregular solitonic solutions: a novel scenario of the nonlinear stage of Modulation Instability