Adaptive trust-region-based algorithm for the discrete eigenvalue evaluation of the direct nonlinear Fourier transform

Abstract

We propose an adaptive method for numerical computation of discrete eigenvalues of the direct nonlinear Fourier transform (NFT). The approach is based on trust region algorithm and modified objective function, which can alleviate the problem of sensitivity to initial values of the Newton–Raphson method, and enhance the robustness as well as reduce the computational complexity. The reliability and performance of the novel, to the best of our knowledge, approach have been demonstrated to a single eigenvalue and multiple eigenvalues of the NFT. Meanwhile, the proposed method can be used not only to solve the complex pulses with a large number of discrete eigenvalues, but also to solve those with eigenvalues having extremely small difference. The results show that the proposed approach represents a significant improvement in comparison with previous reports in the computation accuracy and complexity.