Exact self-similar solutions of the generalized nonlinear Schrödinger equation with distributed coefficients

Self-similar solutions of the generalized Schrödinger equation with distributed coefficients

We present approximate but nevertheless highly accurate self-similar solutions to the generalized linear Schrödinger Equation appropriate to the description of pulse propagation in an optical fibre under the influence of distributed dispersion and gain or attenuation. These new similariton solutions apply for any shape of linearly chirped pulse for any dispersion and gain profiles and are indistinguishable from numerically generated solutions in the majority of practical applications.

Exact multisoliton solutions of the higher-order nonlinear Schrödinger equation with variable coefficients

We investigate the generalized higher-order nonlinear Schrödinger equation with variable coefficients under two sets of parametric conditions. The exact one-soliton solution is presented by the ansatz method for one set of parametric conditions. For the other, exact multisoliton solutions are presented by employing the Darboux transformation based on the Lax pair. As an example, we consider a soliton control system, and the results show that the soliton control system may relax the limitations to parametric conditions. The stability of the solution is discussed numerically; the results reveal that finite initial perturbations, such as amplitude, chirp, or white noise, could not influence the main character of the solution. In addition, the evolution of a quite arbitrary Gaussian pulse and the interaction between neighboring pulses have been studied in detail.

Asymptotic characteristics of parabolic similariton pulses in optical fiber amplifiers

The fundamental asymptotic nature of parabolic similariton pulses in normal-dispersion fiber amplifiers is experimentally demonstrated. With frequency-resolved optical gating characterization measurements with a fixed input pulse energy, the output parabolic pulse characteristics are shown to be invariant with the input pulse profile and duration and to be completely determined only by the amplifier parameters.