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

The Stability of Solutions for the Generalized Degasperis-Procesi Equation with Variable Coefficients

“…Degasperis et al [2] proved the formal integrability of (1) and the existence of the nonsmooth solutions by constructing a Lax pair. In recent years, (1) which plays a similar role in water wave theory as the Camassa-Holm equation has caused extensive concern of many scholars (see [1][2][3][4][5][6][7][8][9][10][11]). For example, Coclite and Karlsen [3] established the well-posedness of 1 ∩ weak solutions for (1).…”

“…Ai and Gui [9] proved global existence of solutions for the viscous Degasperis-Procesi equation and showed that the blow-up phenomena occurs in finite time. Fu et al [11] studied the orbital stability of the peakons for the Degasperis-Procesi equation with a strong dispersive term on the line and proved that the shapes of these peakons were stable under small perturbations.…”