We present in closed form some special travelling-wave solutions (on the realline or on the circle) of a perturbed sine-Gordon equation. The perturbation ofthe equation consists of a constant forcing term $\gamma$ and a lineardissipative term, and the equation is used to describe the Josephson effect inthe theory of superconductors and other remarkable physical phenomena. Wedetermine all travelling-wave solutions with unit velocity (in dimensionlessunits). For $|\gamma|$ not larger than 1 we find families of solutions that areall (except the obvious constant one) manifestly unstable, whereas for$|\gamma|>1$ we find families of stable solutions describing each an array ofevenly spaced kinks.
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