The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics

The Interaction Picture method for solving the generalized nonlinear Schrödinger equation in optics
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求解光学中广义非线性薛定谔方程的交互图法

DOI：
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发表时间：
2016
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通讯作者：
R. Texier
R. Texier
中科院分区：
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文献类型：
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作者：
S. Balac;Arnaud Fernandez;F. Mahé;F. Méhats;R. Texier

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对于求解某些类型的偏微分方程，如用于模拟光纤中波传播的非线性薛定谔方程，“相互作用图”（IP）方法是一种非常有前途的替代方法。该方法显示出有趣的收敛特性，并且可能比成本相当的分步方法（如对称分步方法）提供更精确的数值结果。在这项工作中，我们详细研究了IP方法的数值性质，并对IP方法和对称分步方法进行了精确的比较。
The “interaction picture” (IP) method is a very promising alternative to Split-Step methods for solving certain type of partial differential equations such as the nonlinear Schrodinger equation used in the simulation of wave propagation in optical fibers. The method exhibits interesting convergence properties and is likely to provide more accurate numerical results than cost comparable Split-Step methods such as the Symmetric Split-Step method. In this work we investigate in detail the numerical properties of the IP method and carry out a precise comparison between the IP method and the Symmetric Split-Step method.