Numerical Approximation of the Weakly Damped Nonlinear Shrödinger Equation

Abstract

In this paper we consider the one-dimensional nonlinear Shrödinger equation. The equation includes an absorption term, and the solution is periodically amplified in order to compensate the lose of the energy. The problem describes propagation of a signal in optical fibers. In our previous work we proved that the well-known Crank-Nicolson scheme is unconditionally unstable for this problem. [...].