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Recent studies have revealed that multi-soliton solutions of the nonlinearSchr\"odinger equation, as carriers of information, offer a promising solutionto the problem of nonlinear signal distortions in fiber optic channels. In anynonlinear Fourier transform based transmission methodology seeking to modulatethe discrete spectrum of the multi-solitons, choice of an appropriate windowingfunction is an important design issue on account of the unbounded support ofsuch signals. Here, we consider the rectangle function as the windowingfunction for the multi-solitonic signal and provide the exact solution of theassociated Zakharov-Shabat scattering problem for the windowed/doubly-truncatedmulti-soliton potential. This method further allows us to avoid prohibitivenumerical computations normally required in order to accurately quantify theeffect of time-domain windowing on the nonlinear Fourier spectrum of themulti-solitonic signals. The method devised in this work also applies togeneral type of signals and may prove to be a useful tool in the theoreticalanalysis of such systems.

Exact Solution of the Zakharov-Shabat Scattering Problem for Doubly-Truncated Multi-Soliton Potentials