Adiabatic exponential midpoint rule for the dispersion-managed nonlinear Schrödinger equation
Adiabatic exponential midpoint rule for the dispersion-managed nonlinear Schrödinger equation
复制标题
DOI：
10.1093/imanum/dry045
复制
发表时间：
2018-07
影响因子：
2.1
通讯作者：
T. Jahnke;Marcel Mikl
中科院分区：
文献类型：
--
作者：
T. Jahnke;Marcel Mikl
通过色散管理光纤电缆对长距离数据传输进行建模会导致非线性薛定谔方程，其中线性部分乘以一个大的，不连续的和快速变化的系数函数。典型的解以高频率振荡并且在时间上具有低规律性，使得传统的数值方法受到严格的步长限制并且通常仅以低阶收敛。我们通过扩展Jahnke & Mikl（2018，色散管理非线性薛定谔方程的绝热中点规则）中开发的技术，构造和分析了一个范数守恒，一致收敛的时间积分器，称为绝热指数中点规则。编号。数学、138，975-1009）。这种方法是几个数量级更准确的标准计划的相关参数集。特别是，我们证明了该方法的准确性大大提高，如果在一个特殊的方式选择的步长。
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.