  The Degasperis-Procesi equation can be derived as a member of a one-parameter
family of asymptotic shallow water approximations to the Euler equations with
the same asymptotic accuracy as that of the Camassa-Holm equation. In this
paper, we study the orbital stability problem of the peaked solitons to the
Degasperis-Procesi equation on the line. By constructing a Liapunov function,
we prove that the shapes of these peakon solitons are stable under small
perturbations.
