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We consider here a layered superconductor subject to an externally appliedmoderately-strong electromagnetic field. We predict hysteretic jumps in thedependence of the surface reactance of the superconductor on the amplitude ofthe incident electromagnetic wave. This very unusual nonlinear phenomenon canbe observed in thin superconducting slabs at not very strong ac amplitudes, ifthe frequency of the irradiating field is close to the Josephson plasmafrequency. Using the set of coupled sine-Gordon equations, we derive theexpression for the phase shift of the reflected wave and obtain the conditionsfor the appearance of hysteresis.

Hysteretic jumps in the response of layered superconductors to electromagnetic fields