Using a particular nonlinearity (the "linear + smooth step" model) as an illustrative example, it is demonstrated numerically that cyclic switching between bistable soliton states of the highly-non-linear (generalized) Schriödinger equation can occur. Some important aspects of the switching process, including the nature and role of the intermediate states, are discussed. This numerical simulation may serve as a model of optical switching between distinctly different soliton states in a nonlinear optical fiber and should stimulate the search for the materials and mechanisms with appropriate nonlinearities.
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Enns et al. (1987) studied this question.