  We study the non-linear behavior of the baryon acoustic oscillation in the
power spectrum and the correlation function by decomposing the dark matter
perturbations into the short- and long-wavelength modes. The evolution of the
dark matter fluctuations can be described as a global coordinate transformation
caused by the long-wavelength displacement vector acting on short-wavelength
matter perturbation undergoing non-linear growth. Using this feature, we
investigate the well known cancellation of the high-$k$ solutions in the
standard perturbation theory. While the standard perturbation theory naturally
satisfies the cancellation of the high-$k$ solutions, some of the recently
proposed improved perturbation theories do not guarantee the cancellation. We
show that this cancellation clarifies the success of the standard perturbation
theory at the 2-loop order in describing the amplitude of the non-linear power
spectrum even at high-$k$ regions.We propose an extension of the standard
2-loop level perturbation theory model of the non-linear power spectrum that
more accurately models the non-linear evolution of the baryon acoustic
oscillation than the standard perturbation theory. The model consists of simple
and intuitive parts: the non-linear evolution of the smoothed power spectrum
without the baryon acoustic oscillations and the non-linear evolution of the
baryon acoustic oscillations due to the large-scale velocity of dark matter and
due to the gravitational attraction between dark matter particles. Our extended
model predicts the smoothing parameter of the baryon acoustic oscillation peak
at $z=0.35$ as $\sim 7.7\ {\rm Mpc}/h$ and describes the small non-linear shift
in the peak position due to the galaxy random motions.
