ИСТИНА

At the present time the self-focusing Nonlinear Schrodinger equation is treated as one of the a basic models describing the generation of rouge waves (anomalous waves) in nonlinear media. The Cauchy data for solutions de- scribing the generation of the anomalous waves can be represented as a sum of a constant function and a small perturbation. In the case of periodic per- turbations it is natural to use the finite-gap approach, and the presence of a small parameter allows to obtain simple explicit formulas expressing the algebraic-geometrical data in terms of the Cauchy data modulo higher-order corrections.In particular, this approach provides simple approximate formu- las for the time of first appearance of the rouge wave and for the recurrence times in terms of the Cauchy data.