  Using the Abelian Higgs model, we study the radial excitations of single
vortex and their propagation modes along the vortex line. We call such
beyond-stringy modes {\it peristaltic} modes of single vortex. With the profile
of the static vortex, we derive the vortex-induced potential, i.e.,
single-particle potential for the Higgs and the photon field fluctuations
around the static vortex, and investigate the coherently propagating
fluctuations which corresponds to the vibration of the vortex. We derive,
analyze and numerically solve the field equations of the Higgs and the photon
field fluctuations around the static vortex with various Ginzburg-Landau
parameter $\kappa$ and topological charge $n$. Around the BPS value or critical
coupling $\kappa^2$=1/2, there appears a significant correlation between the
Higgs and the photon field fluctuations mediated by the static vortex. As a
result, for $\kappa^2$=1/2, we find the characteristic {\it new} discrete pole
of the peristaltic mode corresponding to the quasi-bound-state of coherently
fluctuating fields and the static vortex. We investigate its excitation energy,
correlation energy of coherent fluctuations, spatial distributions, and the
resulting magnetic flux behavior in detail. Our investigation covers not only
usual Type-II vortices with $|n|$=1 but also Type-I and Type-II vortices with
$n\in Z$ for the application to various general systems where the vortex-like
objects behave as the essential degrees of freedom.
