  The Degasperis-Procesi (DP) equation is an integrable Camassa-Holm-type model
as an asymptotic approximation for the unidirectional propagation of shallow
water waves. This work is to establish the $L^2\cap L^\infty$ orbital stability
of a wave train containing $N$ smooth solitons which are well separated. The
main difficulties stem from the subtle nonlocal structure of the DP equation.
One consequence is that the energy space of the DE equation based on the
conserved quantity induced by the translation symmetry is only equivalent to
the $L^2$-norm, which by itself can not bound the higher-order nonlinear terms
in the Lagrangian. Our remedy is to introduce \textit{a priori } estimates
based on certain smooth initial conditions. Moreover, another consequence is
that the nonlocal structure of the DP equation significantly complicates the
verification of the monotonicity of local momentum and the positive
definiteness of a refined quadratic form of the orthogonalized perturbation.
