Quasi-linear theory of the nonlinear Schroedinger equation with periodical coefficients

The Schroedinger nonlinear equation (SNE) with the periodical coefficients is studied under the conditions of the large local dispersion. The solution after n periods is represented in the form of the sum of the solution of the SNE linear part and nonlinear correction in the first period multiplated by the number of the n-period. The numerical algorithm is proposed for calculating the quasi-linear solution in the case of the arbitrary initial conditions. Obvious expression of nonlinear correction to the decision for the row of pulses of Gauss forms is obtained