Abstract
In the present study, the solitary wave solutions of modified Degasperis–Procesi equation are developed. Unlike the standard Degasperis–Procesi equation, where multi-peakon solutions arise, the modification caused a change in the characteristic of these peakon solutions and changed it to bell-shaped solitons. By using the extended auxiliary equation method, we deduced some new soliton solutions of the fourth-order nonlinear modified Degasperis–Procesi equation with constant coefficient. These solutions include symmetrical, non-symmetrical kink solutions, solitary pattern solutions, weiestrass elliptic function solutions and triangular function solutions. We discuss the stability analysis for these solutions.