Superfluxons in periodically inhomogeneous long Josephson junctions

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Abstract
Dynamics of a periodic array of fluxons in a dc-driven damped long Josephson junction with an installed periodic lattice of local inhomogeneities are investigated analytically by means of the perturbation theory. In the case when the array and the lattice are commensurable, the array as a whole remains in a pinned state unless the dc bias current density exceeds a certain critical value. It is demonstrated that, in the same time, stable defects in the form of a ‘‘hole’’ or surplus fluxon may propagate along the pinned array. In the long-wave approximation, an evolution equation (an ‘‘elliptic sine-Gordon’’ equation) for local deformations of the array is deduced. That equation supports exact kinklike solutions (‘‘superfluxons’’) which describe the defects mentioned. In the presence of dissipation and dc bias current (with the density smaller than critical), I-V characteristics of the junction corresponding to the motion of a superfluxon are found. The results obtained are in good agreement with results of recent numerical and physical experiments.