Purpose

The purpose of this paper is to obtain the nonlinear Schrodinger equation (NLSE) numerical solutions in the presence of the first-order chromatic dispersion using a second-order, unconditionally stable, implicit finite difference method. In addition, stability and accuracy are proved for the resulting scheme.

Design/methodology/approach

The conserved quantities such as mass, momentum and energy are calculated for the system governed by the NLSE. Moreover, the robustness of the scheme is confirmed by conducting various numerical tests using the Crank-Nicolson method on different cases of solitons to discuss the effects of the factor considered on solitons properties and on conserved quantities.

Findings

The Crank-Nicolson scheme has been derived to solve the NLSE for optical fibers in the presence of the wave packet drift effects. It has been founded that the numerical scheme is second-order in time and space and unconditionally stable by using von-Neumann stability analysis. The effect of the parameters considered in the study is displayed in the case of one, two and three solitons. It was noted that the reliance of NLSE numeric solutions properties on coefficients of wave packets drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws. Accordingly, by comparing our numerical results in this study with the previous work, it was recognized that the obtained results are the generalized formularization of these work. Also, it was distinguished that our new data are regarding to the new communications modes that depend on the dispersion, wave packets drift and nonlinearity coefficients.

Originality/value

The present study uses the first-order chromatic. Also, it highlights the relationship between the parameters of dispersion, nonlinearity and optical wave properties. The study further reports the effect of wave packet drift, dispersions and Kerr nonlinearity play an important control not only the stable and unstable regime but also the energy, momentum conservation laws.

中文翻译：

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求解修正非线性薛定谔方程的 Crank-Nicolson 方案

目的

本文的目的是使用二阶、无条件稳定、隐式有限差分方法获得一阶色散存在时的非线性薛定谔方程 (NLSE) 数值解。此外，证明了所得方案的稳定性和准确性。

设计/方法/方法

计算由 NLSE 控制的系统的守恒量，例如质量、动量和能量。此外，通过使用 Crank-Nicolson 方法对不同情况的孤子进行各种数值测试来讨论所考虑的因素对孤子性质和守恒量的影响，证实了该方案的稳健性。

发现

已经导出 Crank-Nicolson 方案来解决存在波包漂移效应的光纤的 NLSE。通过冯诺依曼稳定性分析，证明了该数值格式在时间和空间上是二阶的，并且是无条件稳定的。研究中考虑的参数的影响在一个、两个和三个孤子的情况下显示。注意到 NLSE 数值解特性对波包漂移系数、色散和克尔非线性的依赖不仅对稳定和不稳定状态而且对能量、动量守恒定律起着重要的控制作用。因此，通过将我们在本研究中的数值结果与以前的工作进行比较，认识到所获得的结果是这些工作的广义公式化。还，

原创性/价值

本研究使用一阶色阶。此外，它还强调了色散参数、非线性和光波特性之间的关系。该研究进一步报告了波包漂移、色散和克尔非线性的影响，不仅对稳定和不稳定状态而且对能量、动量守恒定律起着重要的控制作用。