https://doi.org/10.1140/epjp/s13360-022-02462-8
Regular Article
Bifurcations and exact soliton solutions for generalized Dullin–Gottwald–Holm equation with cubic power law nonlinearity
1
South China Business College, Guangdong University of Foreign Studies, 510545, Guangzhou, China
2
Nanchang Normal College of Applied Technology, 330000, Nanchang, China
3
Jiangxi Vocational College of Mechanical & Electrical Technology, 330000, Nanchang, China
Received:
30
October
2021
Accepted:
8
February
2022
Published online:
18
February
2022
In this paper, we study a system of generalized Dullin–Gottwald–Holm equation with cubic power law nonlinearity. With bifurcation method of dynamical system, we obtain bifurcation of generalized Dullin–Gottwald–Holm equation with Cubic Power Law Nonlinearity. Unfortunately, Hamilton function is a quintic hyper-elliptic function, and it is very difficulty to calculate the integral of the Hamilton function. With the help of Grobner basis elimination method, the modified simplest equation method, and Maple software, we obtain some useful traveling wave solution, including kink wave solutions, anti-kink wave solutions and singular wave solutions. These conclusions may complement and improve previous conclusions. These solutions may help us to understand mechanisms of complex physical phenomena and dynamical processes.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
