Nonlinear Fourier Spectrum of Truncated Multi-Soliton Pulses

Multi-soliton pulses, as special solutions of the Nonlinear Schrodinger Equation (NLSE), are a potential candidate for data modulation in optical fiber communication. Using Nonlinear Fourier Transform (NFT),a multi-soliton pulse have a simple representation in nonlinear Fourier spectrum. For data communication, the exponentially decaying tails of a multi-soliotn must be truncated. Such a windowing changes the nonlinear Fourier spectrum of the pulse. The results of this paper are twofold: (i) we derive the simple closed-form expressions for the nonlinear spectrum, discrete and continuous spectrum, of a symmetrically truncated multi-soliton pulse. We numerically verify the accuracy of the closed-form expressions. (ii) We show how to find, in general, the eigenvalues of the discrete spectrum from the continuous spectrum. We present this method for the application in hand.