  We show that a finite Josephson Junction (JJ) chain, ending with two bulk
superconductors, and with a weak link at its center, may be regarded as a
condensed matter realization of a two-boundary Sine-Gordon model. Computing the
partition function yields a remarkable analytic expression for the DC Josephson
current as a function of the phase difference across the chain. We show that,
in a suitable range of the chain parameters, there is a crossover of the DC
Josephson current from a sinusoidal to a sawtooth behavior, which signals a
transition from a regime where the boundary term is an irrelevant operator to a
regime where it becomes relevant.
