On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation

Badshah, Fazal; Tariq, Kalim U.; Rezazadeh, Hadi; Ilyas, Medhat; Hashemi, Mir Sajjad; Hosseinzadeh, Mohammad Ali

doi:10.22034/cmde.2024.62009.2706

On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation

Document Type : Research Paper

Authors

¹ School of Electrical and Information Engineering, Hubei University of Automotive Technology, Shiyan 442002, People's Republic of China.

² Department of Mathematics, Mirpur University of Science and Technology, Mirpur-10250 (AJK), Pakistan.

³ Faculty of Engineering Modern Technologies, Amol University of Special Modern Technologies, Amol, Iran.

⁴ Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.

10.22034/cmde.2024.62009.2706

Abstract

In this article, the Fordy-Gibbons-Jimbo-Miwa equation is analyzed, a special form of the Kadomtsev-Petviashvili hierarchy equation, which is one of the most prominent nonlinear dynamical models with two spatial and a temporal coordinate that represents the evolution of long, nonlinear, small-amplitude waves with a gradual dependence on the transverse coordinate. The governing model is investigated analytically by employing the extended generalized Riccati equation mapping approach (GREM). Furthermore, the dynamics of several wave structures are visualized in 3D, 2D, and contour forms for a given set of parameters using Mathematica 13.0 to demonstrate their characteristics, which has been achieved by selecting appropriate values of the relevant parameters. These solutions exhibit the characteristics of v-shaped, singular, and multi-bell-shaped, singular periodic, and multi-periodic solitons. Additionally, it has been confirmed that the model under consideration is a stable nonlinear structure by validating the established results. A range of dynamic and static nonlinear equations governing evolutionary phenomena in computational physics and other relevant domains and research areas can be solved using these approaches, as demonstrated by their simplicity, clarity, and effectiveness, as well as the computational complexities and results.

Keywords