A Fast Chebyshev Spectral Method for Nonlinear Fourier Transform

09/09/2019

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by   Vishal Vaibhav, et al.

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In this letter, we present a fast and well-conditioned spectral method based on the Chebyshev polynomials for computing the continuous part of the nonlinear Fourier spectrum. The algorithm achieves a complexity of O(N_iter.N N) per spectral node for N samples of the signal at the Chebyshev nodes where N_iter. is the number of iterations of the biconjugate gradient stabilized method.