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In this work we present a finite difference scheme used to solve a High order Nonlinear Schrodinger Equation with localized damping. These equations can model the propagation of solitons travelling in fiber optics ([3], [10]). The scheme is designed to preserve the numerical en- ergy at L 2 level, and control the energy at H 1 level for a suitable choose on the equation’s parameters, and when there is no damping in effect. Numerical results will be shown.

Finite difference scheme for a high order nonlinear Schrodinger equation with localized damping