Opt Lett. 2019 Nov 1;44(21):5298-5301. doi: 10.1364/OL.44.005298.
We apply the Magnus expansion to the Zakharov-Shabat system, providing a basis for a systematic construction of high-order numerical schemes to solve the direct scattering problem of the integrable one-dimensional nonlinear Schrödinger equation. The presented numerical simulations of previously unreachable wave fields with up to 128 solitons employing second-, fourth-, and sixth-order schemes stresses the need for delicate numerics to identify the eigenvalues and especially phase coefficients. This approach lays the foundation for the study of large optical wave packets, providing fundamental information about their scattering data content and origin of various nonlinear effects.
我们将 Magnus 展开应用于 Zakharov-Shabat 系统，为构造用于求解可积一维非线性 Schrödinger 方程直接散射问题的高阶数值方案提供了基础。利用二阶、四阶和六阶方案对以前无法达到的多达 128 个孤子的波场进行的数值模拟强调了需要进行精细的数值计算以识别特征值，特别是相位系数。这种方法为研究大光学波包奠定了基础，提供了有关它们的散射数据内容和各种非线性效应的起源的基本信息。
