Symmetrical splitting scheme for nonlinear Shrödinger equation - Čiegis, Raimondas; Pakenienė, Violeta (Lietuvos matematikos rinkinys, 2001)
In this paper we consider 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. We present a finite difference approximation by a symetrical splitting scheme. The convergence of the discrete solution is proved.