Simple high-order boundary conditions for computing rogue waves in the nonlinear Schrödinger equation
Simple high-order boundary conditions for computing rogue waves in the nonlinear Schrödinger equation
复制标题
用于计算非线性薛定谔方程中的异常波的简单高阶边界条件
DOI：
10.1016/j.cpc.2019.107109
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发表时间：
2020
影响因子：
6.3
通讯作者：
Jia Yin
中科院分区：
文献类型：
--
作者：
Pengde Wang;Zhiguo Xu;Jia Yin
本文提出了一些简单而精确的人工边界条件，以发展数值方法来计算非线性薛定谔方程（NLSE）的合理的解决方案，模拟流氓波的动力学。为了克服非零的背景条件和代数上的慢衰减率在空间无穷远，我们设计的边界条件，通过一个远场渐近展开制定的合理的解决方案和一些变换休息的振荡的时间。与现有的周期边界条件相比，新边界条件最多可以达到四阶精度，即O（L− 4），区间长度为L，这意味着为了得到预设的精度，可以选择更小的计算区间。同时，它们的形式简单，所以几乎没有任何额外的计算成本来实现的数值方法。然后，我们比较所提出的边界条件和数值方法的效率和精度，并确定最有效和准确的计算NLSE的合理解决方案，并数值研究其稳定性和相互作用。
This paper proposes some simple and accurate artificial boundary conditions in order to develop numerical methods to compute the rational solution of the nonlinear Schrödinger equation (NLSE) modeling the dynamics of rogue waves. To overcome the nonzero background condition and the algebraically slow decaying ratio at spatial infinity, we design the boundary conditions by means of a far field asymptotic expansion formulation of the rational solution and some transformations for resting the oscillation in time. Compared to the existing periodic boundary condition, the proposed boundary conditions can achieve fourth-order accuracy at most, ie, O (L− 4) with the interval length L, which means that for getting the presupposed accuracy, a smaller computational interval can be chosen. Meanwhile, their forms are simple, so there is hardly any additional computational cost to implement the numerical methods. Then we compare the proposed boundary conditions and numerical methods in terms of efficiency and accuracy, and identify the most efficient and accurate one for computing the rational solution of NLSE and numerically study their stability and interaction.