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Badshah, Fazal, Tariq, Kalim U., Rezazadeh, Hadi, Ilyas, Medhat, Hashemi, Mir Sajjad, Hosseinzadeh, Mohammad Ali. (1404). On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation. سامانه مدیریت نشریات علمی, 13(3), 1022-1036. doi: 10.22034/cmde.2024.62009.2706
Fazal Badshah; Kalim U. Tariq; Hadi Rezazadeh; Medhat Ilyas; Mir Sajjad Hashemi; Mohammad Ali Hosseinzadeh. "On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation". سامانه مدیریت نشریات علمی, 13, 3, 1404, 1022-1036. doi: 10.22034/cmde.2024.62009.2706
Badshah, Fazal, Tariq, Kalim U., Rezazadeh, Hadi, Ilyas, Medhat, Hashemi, Mir Sajjad, Hosseinzadeh, Mohammad Ali. (1404). 'On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation', سامانه مدیریت نشریات علمی, 13(3), pp. 1022-1036. doi: 10.22034/cmde.2024.62009.2706
Badshah, Fazal, Tariq, Kalim U., Rezazadeh, Hadi, Ilyas, Medhat, Hashemi, Mir Sajjad, Hosseinzadeh, Mohammad Ali. On the stability analysis and the solitonic wave structures for the Fordy-Gibbons-Jimbo-Miwa equation. سامانه مدیریت نشریات علمی, 1404; 13(3): 1022-1036. doi: 10.22034/cmde.2024.62009.2706

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

Computational Methods for Differential Equations
مقاله 21، دوره 13، شماره 3، مهر 2025، صفحه 1022-1036    اصل مقاله (5.53 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.62009.2706
نویسندگان
Fazal Badshah1؛ Kalim U. Tariq* 2؛ Hadi Rezazadeh* 3؛ Medhat Ilyas2؛ Mir Sajjad Hashemi4؛ Mohammad Ali Hosseinzadeh3
1School of Electrical and Information Engineering, Hubei University of Automotive Technology, Shiyan 442002, People's Republic of China.
2Department of Mathematics, Mirpur University of Science and Technology, Mirpur-10250 (AJK), Pakistan.
3Faculty of Engineering Modern Technologies, Amol University of Special Modern Technologies, Amol, Iran.
4Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran.
چکیده
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.
کلیدواژه‌ها
Fordy-Gibbons-Jimbo-Miwa equation؛ Soliton solutions؛ Kadomtsev-Petviashvili equation؛ Nonlinear dynamics؛ Stability analysis؛ Analytical solutions
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