  The ground state of QCD with two flavors at a finite baryon chemical
potential under rapid rotation is a chiral soliton lattice (CSL) of the $\eta$
meson, consisting of a stack of sine-Gordon solitons carrying a baryon number,
due to the anomalous coupling of the $\eta$ meson to the rotation. In a large
parameter region, the ground state becomes a non-Abelian CSL, in which due to
the neutral pion condensation each $\eta$ soliton decays into a pair of
non-Abelian sine-Gordon solitons carrying $S^2$ moduli originated from
Nambu-Goldstone (NG) modes localized around it, corresponding to the
spontaneously broken vector symmetry SU$(2)_{\rm V}$. There, the $S^2$ modes of
neighboring solitons are anti-aligned, and these modes should propagate in the
transverse direction of the lattice due to the interaction between the $S^2$
modes of neighboring solitons. In this paper, we calculate excitations
including gapless NG modes and excited modes around non-Abelian and Abelian
($\eta$) CSLs, and find three gapless NG modes with linear dispersion relations
(type-A NG modes): two isospinons ($S^2$ modes) and a phonon corresponding to
the spontaneously broken vector SU$(2)_{\rm V}$ and translational symmetries
around the non-Abelian CSL, respectively, and only a phonon for the Abelian CSL
because of the recovering SU$(2)_{\rm V}$. We also find in the deconfined phase
that the dispersion relation of the isospinons becomes of the Dirac type, {\it
i.~e.~} linear even at large momentum.
