Eigenvalue analysis of time separated signals using layer-peeling property

In this paper, we study the Nonlinear Fourier Transform of a signal formed by adding two time-separated pulses. By using the layer peeling property, we show that the eigenvalues of the signal are well approximated by the union of those for the two component pulses separately. The accuracy level of the approximation increases as the component pulses are further separated in time. Scattering coefficients and spectral amplitudes of the signal are also derived, which explain the correlation in eigenvalues, scattering coefficients and spectral amplitudes between the signal and the component pulses.