M. Secondini and E. Forestieri
The nonlinear Schrödinger equation in fiber-optic systems
Received: 27 February 2008
Mathematics Subject Classification (2000): Primary 35Q55 - Secondary 94A05 - 94A40.
Abstract We review some numerical and analytical approaches to the solution of the nonlinear Schrödinger equation for the propagation of optical signals in fiber-optic communication systems. As regards the propagation of deterministic signals, we derive two alternative recursive expression, based on a regular perturbation and a logarithmic perturbation expansion, that, starting from the linear solution, converge to the exact solution of the equation. As regards the propagation of stochastic processes, we review different approaches based on perturbation theory, namely, the continuous wave approximation, the covariance matrix method, and the combined regular-logarithmic perturbation. We discuss accuracy, complexity, and limitations of all the methods and compare them with numerical simulations.