Soliton propagation in a one-dimensional discrete system within self-action mode

Self-action mode demonstrates the soliton dynamics as they propagate through a medium in the absence of external influences or perturbations. Solitons, which are localized waveforms, exhibit remarkable stability and resilience within the self-action mode, maintaining their characteristic shape and velocity despite the dispersive and nonlinear properties of the medium. In the framework of a one-dimensional discrete system, soliton propagation along a succession of distinct sites is described based on the Discrete Nonlinear Schrödinger Equation (DNLSE). The DNLSE is a fundamental model in wave phenomena, encompassing a broad spectrum of physical systems ranging from optics to fluid dynamics.