Abstract
A model, based on the resistively shunted junction theory, is developed and used to study microwave absorption in weak-link Josephson junctions in high-${T}_{c}$ superconductors. Both linear and nonlinear cases of microwave absorption in Josephson junctions are analyzed. A comparison of the model with microwave absorption loop theory is presented along with a general condition for the applicability of both models. The nonlinear case was solved numerically and the threshold points of sharp microwave absorption are presented. At these points, a $2\ensuremath{\pi}$ phase quantization takes place within each microwave cycle, leading to an onset of a sharp rise of absorption. Existence of the $2\ensuremath{\pi}$ dynamic quantization is the key to the interpretation of nonlinear microwave absorption data. The nonlinear microwave absorption model is extended to the study of nonuniformly coupled junctions, and a general statement for the applicability of such a model is presented.
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