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The sine-Gordon equation, used as the representative nonlinear wave equation, presents a bistable behavior resulting from nonlinearity and generating hysteresis properties. We show that the process can be understood in a comprehensive analytical formulation and that it is a generic property of nonlinear systems possessing a natural band gap. The approach allows one to discover that the sine-Gordon equation can work as an ideal switch by reaching a transmissive regime with vanishing driving amplitude.
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Хомерики et al. (2005) studied this question.
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