Modeling long-haul data transmission through dispersion-managed optical fiber cables leads to a nonlinear Schrödinger equation where the linear part is multiplied by a large, discontinuous and rapidly changing coefficient function. Typical solutions oscillate with high frequency and have low regularity in time, such that traditional numerical methods suffer from severe step size restrictions and typically converge only with low order. We construct and analyse a norm-conserving, uniformly convergent time-integrator called the adiabatic exponential midpoint rule by extending techniques developed in Jahnke & Mikl (2018, Adiabatic midpoint rule for the dispersion-managed nonlinear Schrödinger equation. Numer. Math., 138, 975–1009). This method is several orders of magnitude more accurate than standard schemes for a relevant set of parameters. In particular, we prove that the accuracy of the method improves considerably if the step size is chosen in a special way.

中文翻译：

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色散管理非线性薛定ding方程的绝热指数中点法则

通过色散管理的光缆对远程数据传输进行建模会导致一个非线性Schrödinger方程，其中线性部分乘以一个大的，不连续且快速变化的系数函数。典型的解决方案会以高频率振荡，并且时间规律性较低，因此传统的数值方法会受到严格的步长限制，并且通常仅以低阶收敛。通过扩展在Jahnke＆Mikl（2018，色散管理的非线性Schrödinger方程的绝热中点法则）中扩展的技术，我们构建并分析了一个守恒，均匀收敛的时间积分器，称为绝热指数中点法则。Numer。Math。，138，975-1009）。对于一组相关参数，此方法比标准方案要精确几个数量级。特别是，我们证明，如果以特殊方式选择步长，则该方法的准确性将大大提高。