We propose a new method for finding discrete eigenvalues for the direct Zakharov-Shabat problem, based on moving in the complex plane along the argument jumps of the function $a\left(\zeta \right),$ the localization of which does not require great accuracy. It allows to find all discrete eigenvalues taking into account their multiplicity faster than matrix methods and contour integrals. The method shows significant advantage over other methods when calculating a large discrete spectrum, both in speed and accuracy.

中文翻译：

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引入相跳跟踪-直接Zakharov-Shabat问题特征值的快速评估方法

我们提出了一种新的方法，用于寻找直接Zakharov-Shabat问题的离散特征值，该方法基于沿着函数的参数跳转在复杂平面中移动 $\mathrm{一种}（\zeta ），$其定位不需要很高的准确性。与矩阵方法和轮廓积分相比，它可以更快地考虑所有离散特征值的多重性。当计算较大的离散频谱时，该方法在速度和准确性上都显示出优于其他方法的显着优势。