  The Degasperis-Procesi equation is the integrable Camassa-Holm-type model
which is an asymptotic approximation for the unidirectional propagation of
shallow water waves. This work establishes the orbital stability of localized
smooth solitary waves to the Desgasperis-Procesi (DP) equation on the real
line. %extending our previous work on their spectral stability \cite{LLW}. The
main difficulty stems from the fact that the translation symmetry for the DP
equation gives rise to a conserved quantity equivalent to the $L^2$-norm, which
by itself can not bound the higher-order nonlinear terms in the Lagrangian. The
remedy is to observe that, given a sufficiently smooth initial condition
satisfying a measurable constraint, the $L^\infty$ orbital norm of the
perturbation is bounded above by a function of its $L^2$ orbital norm, yielding
the orbital stability in the $L^2\cap L^\infty$ space.
