  Chiral skyrmions are stable particle-like solutions of the Landau-Lifshitz
equation for ferromagnets with the Dzyaloshinskii-Moriya (DM) interaction,
characterized by a topological number. We study the profile of an axially
symmetric skyrmion and give exact formulas for the solution of the
corresponding far-field and near-field equations, in the asymptotic limit of
small DM parameter (alternatively large anisotropy). The matching of these two
fields leads to a formula for the skyrmion radius as a function of the DM
parameter. The derived solutions show the different length scales which are
present in the skyrmion profiles. The picture is thus created of a chiral
skyrmion that is born out of a Belavin-Polyakov solution with an
infinitesimally small radius, as the DM parameter is increased from zero. The
skyrmion retains the Belavin-Polyakov profile over and well-beyond the core
before it assumes an exponential decay; the profile of an axially-symmetric
Belavin-Polyakov solution of unit degree plays the role of the universal core
profile of chiral skyrmions.
