  The Novikov equation is an integrable Camassa-Holm type equation with cubic
nonlinearity. One of the most important features of this equation is the
existence of peakon and multi-peakon solutions, i.e. peaked traveling waves
behaving as solitons. This paper aims to prove both, the orbital and asymptotic
stability of peakon trains solutions, i.e. multi-peakon solutions such that
their initial configuration is increasingly ordered. Furthermore, we give an
improvement of the orbital stability of a single peakon so that we can drop the
non-negativity hypothesis on the momentum density. The same result also holds
for the orbital stability for peakon trains, i.e. in this latter case we can
also avoid assuming non-negativity of the initial momentum density. Finally, as
a corollary of these results together with some asymptotic formulas for the
position and momenta vectors for multi-peakon solutions, we obtain the orbital
and asymptotic stability for initially not well-ordered multipeakons.
