Abstract
We consider here a layered superconductor subject to an externally applied moderately strong electromagnetic field. We predict hysteretic jumps in the dependence of the surface reactance of the superconductor on the amplitude ${H}_{0}$ of the incident electromagnetic wave. This very unusual nonlinear phenomenon can be observed in thin superconducting slabs at not very strong ac amplitudes if the frequency of the irradiating field is close to the Josephson plasma frequency. Using the set of coupled sine-Gordon equations, we derive the expression for the phase shift $\ensuremath{\chi}$ of the reflected wave and obtain the conditions for the appearance of hysteresis in the $\ensuremath{\chi}({H}_{0})$ dependence.
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