1. Introduction . Kerr nonlinearity has become a main obstacle limiting the capacity of long-haul optical fiber communications [ 1 ]. Due to the natural advantage of overcoming the limitations of Kerr nonlinearity, the nonlinear frequency division multiplexing (NFDM) has gotten a lot of attention in recent years [ 2 – 6 ]. It uses the nonlinear Fourier transform (NFT) [ 7 , 8 ] to convert the time domain signal into the nonlinear spectra which evolve linearly and independently along...