  It has been suggested that the wiggle instability (WI) of spiral shocks in a
galactic disk is responsible for the formation of gaseous feathers observed in
grand-design spiral galaxies. We perform both a linear stability analysis and
numerical simulations to investigate the effect of magnetic fields on the WI.
The disk is assumed to be infinitesimally-thin, isothermal, and
non-self-gravitating. We control the strengths of magnetic fields and
spiral-arm forcing using the dimensionless parameters $\beta$ and
$\mathcal{F}$, respectively. By solving the perturbation equations as a
boundary-eigenvalue problem, we obtain dispersion relations of the WI for
various values of $\beta=1-\infty$ and $\mathcal{F}=5\%$ and $10\%$. We find
that the WI arising from the accumulation of potential vorticity at disturbed
shocks is suppressed, albeit not completely, by magnetic fields. The
stabilizing effect of magnetic fields is not from the perturbed fields but from
the unperturbed fields that reduce the density compression factor in the
background shocks. When $\mathcal{F}=5\%$ and $\beta\lesssim 10$ or
$\mathcal{F}=10\%$ and $\beta\sim5-10$, the most unstable mode has a wavelength
of $\sim0.1-0.2$ times the arm-to-arm separation, which appears consistent with
a mean spacing of observed feathers.
