Analytic method for solving the nonlinear Schrodinger equation describing pulse propagation in dispersive optic fibres

The authors give a method for obtaining new exact solutions of the nonlinear Schrodinger equation describing pulse propagation in optical fibres for both the anomalous and the normal dispersion regime. The method is based on the construction of a certain complete integrable finite-dimensional dynamical system whose solution determines the exact solutions of the nonlinear Schrodinger equation. By using the phase diagrams associated with the corresponding nonlinear differential equations they classify all the obtained solutions into one of the following categories: bright or dark solitary waves, bright or dark soliton solutions, rational (algebraic) bright or dark solitons, regular or singular periodic waves and stationary solutions. They give a set of particular solutions which describe the periodic wave patterns that are generated by the temporal self-phase modulation instability, the periodic evolution of bright solitons on a continuous wave background and the collision of two dark waves with equal amplitudes.