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

M.A. Helal ^a , Aly R. Seadawy ^{b , c , ∗} , M. Zekry ^c
a Mathematics Department, Faculty of Science, Cairo University, Giza, Egypt

b Mathematics Department, Faculty of Science, Taibah University, Al-Ula, Saudi Arabia

c Mathematics Department, Faculty of Science, Beni-Suef University, Egypt

Received 28 April 2017; accepted 21 July 2017
Available online 27 July 2017

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 fourthorder 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.
© 2017 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license. ( http://creativecommons.org/licenses/by-nc-nd/4.0/ )
Keywords: Modified Degasperis–Procesi water wave equation; Extended auxiliary equation method; Solitary wave solutions.
PACS: 02.30.Jr; 47.10.A; 47.11.-j; 47.35.Fg