In this work we present a finite difference scheme used to solve a higher order nonlinear Schrödinger equation. These equations are related to models of propagation of solitons travelling in fiber optics. The scheme is designed to preserve the numerical \(L^2\) norm, and control the energy for a suitable choose on the equation’s parameters. We prove the convergence of the numerical solution for this equation in a boundary domain, and we show numerical results displaying conservation properties of the schemes using solitons as initial conditions.

中文翻译：

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高阶非线性Schrödinger方程的有限差分格式

在这项工作中，我们提出了一种用于求解高阶非线性Schrödinger方程的有限差分方案。这些方程与在光纤中传播的孤子的传播模型有关。该方案旨在保留数值\（L ^ 2 \）范数，并控制能量以选择方程式的参数。我们证明了该方程在边界域中的数值解的收敛性，并且我们展示了数值结果，这些结果显示了以孤子为初始条件的方案的守恒性质。