  Dynamics of S=1 antiferromagnetic bond-alternating chains in the dimer phase,
in the vicinity of the critical point with the Haldane phase, is studied by a
field theoretical method. This model is considered to represent the compound
Ni(C$_9$H$_{24}$N$_4$)(NO$_2$)ClO$_4$ (abbreviated as NTENP). We construct the
sine-Gordon (SG) field theory as a low-energy effective model of this system,
starting from a Tomonaga-Luttinger liquid at the critical point. Using the
exact solution of the SG theory, we give a field theoretical picture of the
low-energy excitation spectrum of NTENP. Results derived from our picture are
in a good agreement with results of inelastic neutron scattering experiments on
NTENP and numerical calculation of the dynamical structure factor. Furthermore,
on the basis of the obtained theoretical picture, we predict that the sharp
peaks correspond to a single elementary excitation are absent in the Raman
scattering spectrum of NTENP in contrast to the inelastic neutron scattering
spectrum.
