  Recently Yaakobi and co-workers [Phys. Rev. B 87, 144301 (2013)]
theoretically studied four-wave mixing and parametric amplification in a
nonlinear transmission line consisting of capacitively shunted Josephson
junctions. By deriving and solving the coupled-mode equations, they have
arrived at the conclusion that in a wide frequency range around the pump
frequency exponential parametric gain (in which the signal grows exponentially
with distance) can be achieved. However, we have found a mathematical error in
their derivation of the coupled-mode equations (Equation (A13)), which leads to
the wrong expression of the gain factor and invalidates their conclusions on
the gain and bandwidth. In this comment, we present the correct expression for
the parametric gain. We show that for a transmission line with weak dispersion
or positive dispersion ($\Delta k>0 $), as is the case discussed by Yaakobi et
al, while quadratic (power) gain can occur around the pump frequency,
exponential gain is impossible. Furthermore, for a transmission line with
proper intrinsic or engineered dispersion, exponential gain occurs at
frequencies where the phase matching condition is met, while around the pump
frequency the gain is still quadratic.
