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首页> 外文期刊>International journal of numerical methods for heat & fluid flow >Crank-Nicolson Scheme for Solving the Modified Nonlinear Schrodinger Equation
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Crank-Nicolson Scheme for Solving the Modified Nonlinear Schrodinger Equation

机译：求解改进的非线性Schrodinger方程的曲柄 - 尼古尔森方案

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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 generalised 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.
机译：目的 - 本文的目的是在使用二阶，无条件稳定的隐式有限差分方法存在一阶色散存在下获得非线性Schrodinger方程（NLSE）数值溶液。此外，证明了所得方案的稳定性和准确性。设计/方法/方法 - 为NLSE管理的系统计算了质量，动量和能量等保守数量。此外，通过在不同孤子的不同情况下进行各种数值测试来证实方案的稳健性来证实，讨论孤子性质和保守数量的因子对所考虑的因子的影响。调查结果 - 已经得出了曲柄 - 尼古尔森方案，以解决波包漂移效果的存在下的光纤中的NLSE。已经成立，通过使用von-neumann稳定性分析，数值方案是时间和空间的二阶和空间，无条件稳定。在研究中考虑的参数的效果显示在一个，两个和三个孤子的情况下。有望指出，NLSE数字解决方案属性对波包漂移，分散和克尔非线性的系数不仅发挥了重要控制，不仅是稳定和不稳定的制度，而且是能量，动量保护法。因此，通过将我们的数值结果与先前的作品进行比较，得到了所得结果是这些工作的广义惯性化。此外，区分的是，我们的新数据关于依赖于色散，波浪分组漂移和非线性系数的新的通信模式。原创性/值 - 本研究使用一阶彩色。此外，它突出了色散，非线性和光波属性参数之间的关系。该研究进一步报道了波浪包漂移，分散和克尔非线性的影响不仅发挥了重要控制，不仅是稳定和不稳定的制度，而且是能量，动量保护法。

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