New Fast Exponential Splitting Schemes for Nonlinear Fourier Transform

The nonlinear Fourier transform (NFT) is a method for analyzing signal structures influenced by the nonlinear Schrödinger equation (NLSE). Enhancing the performance and accuracy of NFT algorithms is crucial in fiber optics. We propose a method to identify all suitable symmetric exponential splitting schemes that enhance the speed of fast NFT (FNFT) algorithms while maintaining low numerical complexity. The schemes we developed performed well in numerical tests, comparing favorably with other fast 4th order NFT algorithms.