Josephson superlattices and low-amplitude gap solitons

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Abstract
We have examined the amplitude dependence of the transmission properties in the natural gap of a finite Josephson transmission line and in the first artificial gap of a finite Josephson superlattice. We show that the nonlinear transmission response of both systems exhibits gap-soliton-mediated bistability and hysteresis and can approach unity, once the amplitude of the incoming wave is greater than a certain threshold which is frequency dependent and also decreases with the length of the system. Our computer experiments on the dynamics of wave transmission, which show how the systems would behave in practice, are in good agreement with our calculations and the theoretical predictions in the literature for other kinds of superlattices. We have observed that the modulational instability in the Benjamin-Feir sense which may appear in some computer experiments is eliminated if one considers weak dissipative systems.

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