  The long-time evolution of the KdV-type solitons propagating in ferromagnetic
materials is considered trough a multi-time formalism, it is governed by all
equations of the KdV Hierarchy. The scaling coefficients of the higher order
time variables are explicitly computed in terms of the physical parameters,
showing that the KdV asymptotic is valid only when the angle between the
propagation direction and the external magnetic field is large enough. The
one-soliton solution of the KdV hierarchy is written down in terms of the
physical parameters. A maximum value of the soliton parameter is determined,
above which the perturbative approach is not valid. Below this value, the KdV
soliton conserves its properties during an infinite propagation time.
