Finite difference scheme for a high order nonlinear Schrödinger equation with localized damping
DOI:
https://doi.org/10.24193/subbmath.2019.2.03Keywords:
High order, nonlinear Schrödinger equation, localized damping, dissipation, finite difference methods.Abstract
In this work we present a finite difference scheme used to solve a High order Nonlinear Schrödinger Equation. These equations can model the propagation of solitons travelling in fiber optics ([3], [11]). The scheme is designed to preserve the numerical energy at L2 level, and control the energy at H1 level for a suitable choose on the equation’s parameters. We show numerical results dis- playing conservation properties of the schemes using solitons as initial conditions.
Mathematics Subject Classification (2010): 35Q55, 65-06, 65M06, 65Z05.
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