Finite difference scheme for a high order nonlinear Schrödinger equation with localized damping - CAVALCANTI, Marcelo M.; CORRÊA, Wellington J.; SEPÚLVEDA C., Mauricio A.; VÉJAR ASEM, Rodrigo (Studia Universitatis Babeș-Bolyai Mathematica, 2019)
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.