AI 中文总结
该研究提出了一种用于暗孤子的数值直接散射变换方案，可表征散焦介质中的非线性相干结构，经测试可准确恢复孤子参数，为分析复杂波场数据提供可靠方法。
AI 中文摘要
我们提出了一种针对非线性薛定谔方程暗孤子的数值直接散射变换方案，该方案可识别并完整表征具有连续波（CW）背景的散焦介质中的非线性相干结构。我们的方案基于数值求解带有连续波边界条件的辅助Zakharov-Shabat散射问题，以及解析推导得到的、将转移矩阵元素与暗孤子和连续谱波的散射数据关联起来的表达式。为测试该方法，我们考虑了散射问题的两种解析可解情形：i）连续波背景中的矩形凹陷，ii）双曲正切凹陷，这两种凹陷可包含任意数量的暗孤子，且具有已知的散射数据。我们重新推导了解析过程，得到了由离散本征值和归一化常数表示的完整孤子参数集。通过为直接散射变换算法补充高精度算术以准确恢复孤子归一化常数，我们提供了一种可靠方法，用于分析光学、流体动力学及其他物理系统中复杂波场的数值或自然实验数据。
英文摘要
We introduce a numerical direct scattering transform scheme for dark solitons of the nonlinear Schrodinger equation, enabling the identification and complete characterization of nonlinear coherent structures in defocusing media with a continuous-wave (CW) background. Our scheme is based on numerically solving the auxiliary Zakharov-Shabat scattering problem with CW boundary conditions and on analytically derived expressions that relate the elements of the transfer matrix to the scattering data for dark solitons and continuous-spectrum waves. To test our approach, we consider two analytically solvable cases of the scattering problem: i) rectangular, and ii) hyperbolic tangent hollows in the CW background, which can contain an arbitrary number of dark solitons, with known scattering data. We revisit the analytical derivations and obtain a complete set of soliton parameters represented by discrete eigenvalues and norming constants. By supplementing the direct scattering transform algorithm with high-precision arithmetic to accurately recover soliton norming constants, we provide a robust method to analyze data from numerical or natural experiments on complex wave fields in optical, hydrodynamical, and other physical systems.
Comments12 pages, 3 figures
