# Fast Nonlinear Fourier Transform Algorithms Using Higher Order Exponential Integrators

## TL;DR

This paper introduces fast nonlinear Fourier transform algorithms using higher order exponential integrators that significantly improve accuracy while maintaining low computational complexity, benefiting applications like fiber optic communications.

## Contribution

The paper proposes novel fast NFT algorithms based on higher order exponential integrators, achieving superior accuracy with comparable computational efficiency.

## Key findings

- Achieve orders of magnitude better accuracy than existing methods.
- Maintain low computational complexity comparable to current algorithms.
- Demonstrate effectiveness through extensive numerical comparisons.

## Abstract

The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of highly accurate low-complexity algorithms remains a challenge. In this paper, we present new fast forward NFT algorithms that achieve accuracies that are orders of magnitudes better than current methods, at comparable run times and even for moderate sampling intervals. The new algorithms are compared to existing solutions in multiple, extensive numerical examples.