Fast nonlinear Fourier transform algorithm for reconstruction of optical data from nonlinear spectra of the Manakov system

Abstract

We propose a high-precision algorithm for solving the three-component Gelfand–Levitan–Marchenko equations (GLME) associated with the Manakov system, which describes the behavior of light waves through the optical fibers. The algorithm generalizes the high-order generalized Toeplitz inner-bordering method for solving the two-component GLME associated with the nonlinear Schrödinger equation. Numerical experiments have shown that the proposed algorithm makes it possible to increase the accuracy of solving the GLME associated with Manakov system up to the sixth order.