Exact Self-Similar Solutions of the Generalized Nonlinear Schrödinger Equation with Distributed Coefficients

A broad class of exact self-similar solutions to the nonlinear Schrödinger equation (NLSE) with distributed dispersion, nonlinearity, and gain or loss has been found. Appropriate solitary wave solutions applying to propagation in optical fibers and optical fiber amplifiers with these distributed parameters have also been studied. These solutions exist for physically realistic dispersion and nonlinearity profiles in a fiber with anomalous group velocity dispersion. They correspond either to compressing or spreading solitary pulses which maintain a linear chirp or to chirped oscillatory solutions. The stability of these solutions has been confirmed by numerical simulations of the NLSE.

Figure 1

Comparison of analytical solution (circles) with numerical simulation (solid line) for a propagating solitary pulse in an amplifier with constant loss (a) or gain (b) and distributed dispersion and nonlinearity.