  To address questions about the physical nature and origin of spiral arms in
galaxies, it is necessary to measure their dynamical properties, such as the
angular speed, $\Omega_p$, or the corotation radius. Observations suggest that
galaxies may contain several independent spiral patterns simultaneously. It was
shown that so-called non-linear resonance coupling plays an important role in
such systems. We aim to identify cases of independent spiral patterns for
galaxies with a flat rotation curve and to investigate what relative pattern
velocities they might have for all possible cases of coupling between the main
resonances. We solved equations for the main resonance positions (1:1, 2:1,
4:1) and estimated the ratio $\varpi$ of the corotation radii for two
subsequent patterns. For six close galaxies with flat rotation curves, we
collected the measurements of the corotation radii in the literature, using at
least three different methods in each case for credibility. We found at least
two independent spiral patterns for each galaxy and measured the $\varpi$
ratios. For three cases, we obtained $\varpi>3$, indicating that it would be
difficult to fit two or even more spiral patterns in the disc. These ratios
have been used to derive the wind-up time for spirals, estimated to be several
galactic rotations. We find that three pairs of coupling cases, including those
that have been vastly acknowledged in galaxies, namely, $OLR_{in}=CR_{out} \&
CR_{in}=IUHR_{out}$, have very close $\varpi$ ratios; hence, they ought to be
found simultaneously, as observed. We find a strongly confirmed apparent
resonance coupling for six galaxies and we show that the observed $\varpi$ is
in agreement with theory. In two of them, we identified a previously unreported
form of simultaneous coupling, namely, $OLR_{in}=OUHR_{out} \&
OUHR_{in}=CR_{out}$. This result was also predicted from the proximity of
$\varpi$.
