  We study the capillary retraction of a Newtonian semi-infinite liquid
filament through analytical methods. We derive a long-time asymptotic-state
expansion for the filament profile using a one-dimensional free-surface slender
cylindrical flow model based on the three-dimensional axisymmetric
Navier-Stokes equations. The analysis identifies three distinct length and time
scale regions in the retraction domain: a steady filament section, a growing
spherical blob, and an intermediate matching zone. We show that liquid
filaments naturally develop travelling capillary waves along their surface and
a neck behind the blob. We analytically prove that the wavelength of the
capillary waves is approximately 3.63 times the filament's radius at the
inviscid limit. Additionally, the waves' asymptotic wavelength, decay length,
and the minimum neck size are analysed in terms of the Ohnesorge number.
Finally, our findings are compared with previous results from the literature
and numerical simulations in Basilisk obtaining a good agreement. This analysis
provides a full picture of the recoiling process going beyond the classic
result of the velocity of retraction found by Taylor and Culick.
