### Abstract

It is demonstrated in this letter that linear multistep methods for integrating ordinary differential equations can be used to develop a family of fast forward scattering algorithms with higher orders of convergence. Excluding the cost of computing the discrete eigenvalues, the nonlinear Fourier transform (NFT) algorithm thus obtained has a complexity of O(KN+C_{p}Nlog^{2}N) such that the error vanishes as mathop O(N^{-p}) where p ϵ {1,2,3,4} and K is the number of eigenvalues. Such an algorithm can be potentially useful for the recently proposed NFT-based modulation methodology for optical fiber communication. The exposition considers the particular case of the backward differentiation formula (C_{p}=p^{3}) and the implicit Adams method (C_{p}=(p-1^{3},p>1) of which the latter proves to be the most accurate family of methods for fast NFT.

Original language | English |
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Pages (from-to) | 700-703 |

Journal | IEEE Photonics Technology Letters |

Volume | 30 |

Issue number | 8 |

DOIs | |

Publication status | Published - 2018 |

### Keywords

- Nonlinear Fourier transform
- Zakharov-Shabat scattering problem

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## Cite this

*IEEE Photonics Technology Letters*,

*30*(8), 700-703. https://doi.org/10.1109/LPT.2018.2812808