TRANSFORMATION OF A LINEAR WAVE BY A LOCAL NONLINEAR ELEMENT

We consider the scattering problem for the D'Alembert equation with a local nonlinear sine term, which is a simplest model of a dispersionless transmission line with an inserted Josephson junction. The incident wave is taken in the purely ac form. We demonstrate that, when its amplitude exceeds a certain threshold that depends upon the value of a coefficient in front of the nonlinear term, the transmitted and reflected waves contain both ac and de components, the latter meaning a nonzero mean value of the time derivative.