Encoding of information in nonlinear fiber lines, based on the inverse scattering problem method

Remarkable mathematical properties of the integrable nonlinear Schrödinger equation (NLSE) can offer advanced solutions for the mitigation of nonlinear signal distortions in optical fiber links. Fundamental optical soliton, continuous, and discrete eigenvalues of the nonlinear spectrum have already been considered for the transmission of information in fiber-optic channels. We propose to apply signal modulation to the kernel of the Gelfand-Levitan-Marchenko equations that offers the advantage of a relatively simple decoder design. We describe an approach based on exploiting the general N-soliton solution of the NLSE for simultaneous coding of N symbols involving 4×N coding parameters. We introduce a Soliton Orthogonal Frequency Division Multiplexing (SOFDM) method. This method is based on the choice of identical imaginary parts of the N-soliton solution eigenvalues, corresponding to equidistant soliton frequencies, making it similar to the conventional OFDM scheme, thus, allowing for the use of the efficient fast Fourier transform algorithm. Applications of the inverse scattering method for solving the Cauchy problem for the Helmholtz equation and the Manakov model are also briefly presented.