Stability analysis solutions of the nonlinear modified Degasperis–Procesi water wave equation

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.