Opt Lett. 2018 Aug 1;43(15):3690-3693. doi: 10.1364/OL.43.003690.
We propose a novel algorithm for the numerical computation of discrete eigenvalues in the Zakharov-Shabat problem. Our approach is based on contour integrals of the nonlinear Fourier spectrum function in the complex plane of the spectral parameter. The reliability and performance of the new approach are examined in application to a single eigenvalue, multiple eigenvalues, and the degenerate breather's multiple eigenvalue. We also study the impact of additive white Gaussian noise on the stability of numerical eigenvalues computation.
我们提出了一种用于数值计算扎哈罗夫-沙巴特问题中离散特征值的新算法。我们的方法基于非线性傅里叶谱函数在谱参数复平面上的围道积分。该新方法的可靠性和性能通过应用于单个特征值、多个特征值以及简并呼吸子的多个特征值进行了检验。我们还研究了加性白高斯噪声对数值特征值计算稳定性的影响。
