Dynamics of the long Josephson junctions

Static and dynamic properties of long sandwich-type Josephson junctions have been analyzed. These junctions, both rectangular ("uniform") and non-rectangular ("shaped"), can be described by the one-dimensional equation for the phase difference ϕ (x,t), with the coefficients generally dependent on x. The variation of these coefficients reflects that of effective junction inductance, capacitance, critical current density and injected current density, along the junction length L. If
L \gg \lambda_{J}
, the equation for ϕ (x,t) can be reduced to a simpler "hydrodynamic-type" equation for the Josephson vortex density. Coefficients of this reduced equation have been found analytically for the limit cases. The static version of the reduced equation has been used for calculating the threshold characteristics of the shaped Josephson junctions, including the amplitude of "side-lobes". The dynamic version of the equation has been used for the description of the I-V curves of the uniform junctions; viscous flux flow, Eck peak and "displaced linear branch" are particularly discussed.