Abstract This paper proposes some simple and accurate artificial boundary conditions in order to develop numerical methods to compute the rational solution of the nonlinear Schrodinger 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, i.e., 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.

中文翻译：

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用于计算非线性薛定谔方程中的流氓波的简单高阶边界条件

摘要 本文提出了一些简单而准确的人工边界条件，以开发数值方法来计算非线性薛定谔方程 (NLSE) 的有理解，该方程模拟流氓波的动力学。为了克服空间无穷远的非零背景条件和代数缓慢衰减比，我们通过有理解的远场渐近展开公式和一些用于及时停止振荡的变换来设计边界条件。与现有的周期性边界条件相比，所提出的边界条件最多可以达到四阶精度，即区间长度为 L 的 O ( L − 4 ) ，这意味着为了获得预设精度，可以采用更小的计算区间选择了。同时，它们的形式很简单，所以几乎没有任何额外的计算成本来实现数值方法。然后我们在效率和精度方面比较了所提出的边界条件和数值方法，并确定了计算 NLSE 有理解的最有效和最准确的方法，并数值研究了它们的稳定性和相互作用。