Quasilinear theory for the nonlinear Schrödinger equation with periodic coefficients

The nonlinear Schrödinger equation with periodic coefficients is analyzed under the condition of large variation in the local dispersion. The solution after $n$ periods is represented as the sum of the solution to the linear part of the nonlinear Schrödinger equation and the nonlinear first-period correction multiplied by the number of periods $n$. An algorithm for calculating the quasilinear solution with arbitrary initial conditions is proposed. The nonlinear correction to the solution for a sequence of Gaussian pulses is obtained in the explicit form.