Fundamental properties of solitons in the recently introduced split-step model (SSM) are investigated. The SSM is a system that consists of periodically alternating dispersive and nonlinear segments, a period being of the same order of magnitude as the soliton’s dispersion length. The model including fiber loss and gain can always be reduced to its lossless version. First, we develop a variational approximation that makes it possible to explain the existence of SSM solitons that were originally found solely in numerical form. Overall dynamic behavior of a SSM is described by a phase diagram that identifies an established state (stationary soliton, breather with long-period oscillations, splitting into several pulses, or decay into radiation) depending on the amplitude and the width of the initial pulse. In particular, strong saturation in the dependence of the amplitude of the established soliton on the amplitude of the initial pulse is found. The results clearly show some similarities and drastic differences between the SSM and the ordinary soliton model based on the nonlinear Schrödinger equation. A random version of the SSM is introduced, with the length of the system’s cell uniformly distributed in some interval, which is a relevant case for applications to fiber-optic telecommunication networks. It is found that the dynamics of the SSM solitons as well as interactions between them in random systems (both single-channel and multichannel systems) are virtually the same as in their regular counterparts.
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