  We explore the class of exponential integrators known as exponential time
differencing (ETD) method in this letter to design low complexity nonlinear
Fourier transform (NFT) algorithms that compute discrete approximations of the
scattering coefficients in terms of the Chebyshev polynomials for real values
of the spectral parameter. In particular, we discuss ETD Runge-Kutta methods
which yield algorithms with complexity $O(N\log^2N)$ (where $N$ is the number
of samples of the signal) and an order of convergence that matches the
underlying one-step method.
