Orbital stability of peakons for the Degasperis–Procesi equation with strong dispersion

In this paper, we study the orbital stability of the peakons for the Degasperis–Procesi equation with a strong dispersive term on the line. Using the method in [Z. Lin, Y. Liu, Stability of peakons for the Degasperis–Procesi equation, Comm. Pure Appl. Math. 62 (2009) 125–146], we prove that the shapes of these peakons are stable under small perturbations. Some previous results are extended.