Exact solutions of nonlinear Schrödinger equation for positive group velocity dispersion

A method is given for obtaining new exact solutions of nonlinear Schrödinger equation describing the propagation of pulses in optical fibers for positive group-velocity dispersion. The method is based on the construction of a certain complete integrable finite-dimensional dynamical system, whose solutions determine the exact solutions of nonlinear Schrödinger equation. The set of exact analytic solutions contains dark solitary waves, dark soliton, periodic, and stationary solutions which are very important from a physical point of view.