دانشگاه تبریز
فهرست نشریات دارای اعتبار وزارت علوم، تحقیقات و فناوری
پایگاه استنادی علوم جهان اسلام (ISC)

 آمار

تعداد نشریات45
تعداد شماره‌ها1,417
تعداد مقالات17,482
تعداد مشاهده مقاله56,413,918
تعداد دریافت فایل اصل مقاله18,719,163
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
مراجع
  • [1] H. Ahmad, K. U. Tariq, and S. M. Raza Kazmi, Stability, modulation instability and traveling wave solutions of (3+ 1) dimensional  Schrödinger model in physics, Optical and Quantum Electronics, 56(7) (2024), 1237.
  • [2] N. H. Ali, S. A. Mohammed, and J. Manafian, Study on the simplified MCH equation and the combined KdV– mKdV equations with solitary wave solutions, Partial Differential Equations in Applied Mathematics, 9 (2024), 100599.
  • [3] F. Badshah, K. U. Tariq, A. Henaish, and J. Akhtar, On some soliton structures for the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in mathematical physics, Mathematical Methods in the Applied Sciences, 47(6) (2024), 4756–4772.
  • [4] F. Badshah, K. U. Tariq, M. Inc, and R. Javed, On soliton solutions of Fokas dynamical model via analytical approaches, Optical and Quantum Electronics, 56(5) (2024), 743.
  • [5] F. Badshah, K. U. Tariq, M. Inc, and M. Zeeshan, On the solitonic structures for the fractional Schrödinger–Hirota equation, Optical and Quantum Electronics, 56(5) (2024), 848.
  • [6] F. Badshah, K. U. Tariq, A. Bekir, R. Nadir Tufail, and H. Ilyas, Lump, periodic, travelling, semi-analytical solutions and stability analysis for the Ito integro-differential equation arising in shallow water waves, Chaos, Solitons & Fractals, 182 (2024), 114783.
  • [7] A. Bekir, On traveling wave solutions to combined KdV–mKdV equation and modified Burgers–KdV equation, Communications in Nonlinear Science and Numerical Simulation, 14(4) (2009), 1038–1042.
  • [8] A. Cevikel, Traveling wave solutions of Fordy–Gibbons equation, Modern Physics Letters B, 38(4) (2024), 2450448.
  • [9] P. K. Das, S. M. Mirhosseini-Alizamini, D. Gholami, and H. Rezazadeh, A comparative study between obtained solutions of the coupled Fokas–Lenells equations by Sine-Gordon expansion method and rapidly convergent approximation method, Optik, 283 (2023), 170888.
  • [10] B. Dorizzi, B. Grammaticos, A. Ramani, and P. Winternitz, Are all the equations of the Kadomtsev–Petviashvili hierarchy integrable, Journal of Mathematical Physics, 27(12) (1986), 2848–2852.
  • [11] A. Fordy and A. Pickering, Analysing negative resonances in the Painleve test, Physics Letters A, 160(4) (1991), 347–354.
  • [12] Y. Gu, S. Malmir, J. Manafian, O. A. Ilhan, A. Alizadeh, and A. J. Othman, Variety interaction between k-lump and k-kink solutions for the (3+1)-D Burger system by bilinear analysis, Results in Physics, 43 (2022), 106032.
  • [13] T. Han, K. Zhang, Y. Jiang, and H. Rezazadeh, Chaotic Pattern and Solitary Solutions for the (21)-Dimensional Beta-Fractional Double-Chain DNA System, Fractal and Fractional, 8(7) (2024), 415.
  • [14] R. Hirota, The direct method in soliton theory, Cambridge University Press, Cambridge, 2004.
  • [15] K. Hosseini, E. Hincal, S. Salahshour, M. Mirzazadeh, K. Dehigia, and B. J. Nath, On the dynamics of soliton waves in a generalized nonlinear Schrödinger equation, Optik, (2022), 170215.
  • [16] L. Hu, D. S. Hecht, and G. Gruner, Carbon nanotube thin films: fabrication, properties, and applications, Chemical reviews, 110(10) (2010), 5790–5844.
  • [17] X. B. Hu, D. L. Wang, H. W. Tam, and W. M. Xue, Soliton solutions to the Jimbo–Miwa equations and the Fordy–Gibbons–Jimbo–Miwa equation, Physics Letters A, 262(4-5) (1999), 310–320.
  • [18] M. Jimbo and T. Miwa, Solitons and infinite dimensional Lie algebras, Publications of the Research Institute for Mathematical Sciences, 19(3) (1983), 943–1001.
  • [19] B. Karaman, The use of improved-F expansion method for the time-fractional Benjamin–Ono equation, Revista de la Real Academia de Ciencias Exactas, Fısicas y Naturales. Serie A. Matematicas, 115(3) (2021), 128.
  • [20] M. Lakestani, J. Manafian, A. R. Najafizadeh, and M. Partohaghighi, Some new soliton solutions for the nonlinear fifth-order integrable equations, Computational Methods for Differential Equations, 10(2) (2022), 445–460.
  • [21] X. Liang, Z. Cai, M. Wang, X. Zhao, H. Chen, and C. Li, Chaotic oppositional sine–cosine method for solving global optimization problems, Engineering with Computers, (2022), 1–17.
  • [22] Q. Liu, A modified Jacobi elliptic function expansion method and its application to Wick-type stochastic KdV equation, Chaos, Solitons & Fractals, 32(3) (2007), 1215–1223.
  • [23] J. Manafian and M. Lakestani, Application of tan (ϕ/2)-expansion method for solving the Biswas–Milovic equation for Kerr law nonlinearity, Optik, 127(4) (2016), 2040–2054.
  • [24] J. Manafian and M. Lakestani, Abundant soliton solutions for the Kundu–Eckhaus equation via tan (ϕ (ξ)) expansion method, Optik, 127(14) (2016), 5543–5551.
  • [25] J. Manafian and M. Lakestani, Optical soliton solutions for the Gerdjikov–Ivanov model via tan (ϕ/2)-expansion method, Optik, 127(20) (2016), 9603–9620.
  • [26] J. Manafian and M. Lakestani, N-lump and interaction solutions of localized waves to the (2+1)-dimensional variable-coefficient Caudrey–Dodd–Gibbon–Kotera–Sawada equation, Journal of Geometry and Physics, 150 (2020), 103598.
  • [27] J. Manafian, L. A. Dawood, and M. Lakestani, New solutions to a generalized fifth-order KdV like equation with prime number p= 3 via a generalized bilinear differential operator, Partial Differential Equations in Applied Mathematics, 9 (2024), 100600.
  • [28] B. Radha and C. Duraisamy, The homogeneous balance method and its applications for finding the exact solutions for nonlinear equations, Journal of Ambient Intelligence and Humanized Computing, 12 (2021), 6591–6597.
  • [29] H. Rezazadeh, A. Korkmaz, M. Eslami, and S. M. Mirhosseini-Alizamini, A large family of optical solutions to Kundu–Eckhaus model by a new auxiliary equation method, Optical and Quantum Electronics, 51 (2019), 1–12.
  • [30] S. T. R. Rizvi, A. R. Seadawy, S. Ahmed, and K. Ali, Einstein’s vacuum field equation: lumps, manifold periodic, generalized breathers, interactions and rogue wave solutions, Optical and Quantum Electronics, 55(2) (2023), 181.
  • [31] S. T. R. Rizvi, A. R. Seadawy, S. Ahmed, M. Younis, and K. Ali, Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation, Chaos, Solitons & Fractals, 151 (2021), 111251.
  • [32] A. Seadawy, A. Ali, A. Altalbe, and A. Bekir, Exact solutions of the (3+ 1)-generalized fractional nonlinear wave equation with gas bubbles, Scientific Reports, 14(1) (2024), 1862.
  • [33] L. Tang, Dynamical behavior and multiple optical solitons for the fractional Ginzburg–Landau equation with βderivative in optical fibers, Optical and Quantum Electronics, 56(2) (2024), 175.
  • [34] K. U. Tariq and R. Javed, Some traveling wave solutions to the generalized (3+ 1)-dimensional Korteweg–de Vries–Zakharov–Kuznetsov equation in plasma physics, Mathematical Methods in the Applied Sciences, 46(12) (2023), 12200–12216.
  • [35] K. U. Tariq, E. Tala-Tebue, H. Rezazadeh, M. Younis, A. Bekir, and Y. Chu, Construction of new exact solutions of the resonant fractional NLS equation with the extended Fan sub-equation method, Journal of King Saud UniversityScience, 33(8) (2021), 101643.
  • [36] K. U. Tariq, A.-M. Wazwaz, and R. Javed, Construction of different wave structures, stability analysis and modulation instability of the coupled nonlinear Drinfel’d–Sokolov–Wilson model, Chaos, Solitons & Fractals, 166 (2023), 112903.
  • [37] K. U. Tariq, A. M. Wazwaz, and S. M. Raza Kazmi, On the dynamics of the (2+ 1)-dimensional chiral nonlinear Schrödinger model in physics, Optik, 285 (2023), 170943.
  • [38] K. J. Wang, Resonant Y-type soliton, X-type soliton and some novel hybrid interaction solutions to the (3+ 1)-dimensional nonlinear evolution equation for shallow-water waves, Physica Scripta, 99(2) (2024), 025214.
  • [39] M. Wang, B. Tian, and T. Y. Zhou, Darboux transformation, generalized Darboux transformation and vector breathers for a matrix Lakshmanan-Porsezian-Daniel equation in a Heisenberg ferromagnetic spin chain, Chaos, Solitons & Fractals, 152 (2021), 111411.
  • [40] A. M. Wazwaz, Multiple-soliton solutions for the Calogero–Bogoyavlenskii–Schiff, Jimbo–Miwa and YTSF equations, Applied Mathematics and Computation, 203(2) (2008), 592–597.
  • [41] J. Weiss, M. Tabor, and G. Carnevale, The Painleve property for partial differential equations, Journal of Mathematical Physics, 24(3) (1983), 522–526.
  • [42] U. Younas, J. Ren, and M. Bilal, Dynamics of optical pulses in fiber optics, Modern Physics Letters B, 36(05) (2022), 2150582.
  • [43] U. Younas, T. A. Sulaiman, and J. Ren, Propagation of M-truncated optical pulses in nonlinear optics, Optical and Quantum Electronics, 55(2) (2023), 102.
  • [44] U. Younas, T. A. Sulaiman, and J. Ren, Diversity of optical soliton structures in the spinor Bose–Einstein condensate modeled by three-component Gross–Pitaevskii system, International Journal of Modern Physics B, 37(01) (2023), 2350004.
  • [45] U. Younas, T. A. Sulaiman, J. Ren, and A. Yusuf, Lump interaction phenomena to the nonlinear ill-posed Boussinesq dynamical wave equation, Journal of Geometry and Physics, 178 (2022), 104586.
  • [46] E. M. E. Zayed, M. E. Alngar, R. Shohib, and A. Biswas, Highly dispersive solitons in optical couplers with metamaterials having Kerr law of nonlinear refractive index, Inst Physical Optics, (2024).
  • [47] M. Zhang, X. Xie, J. Manafian, O. A. Ilhan, and G. Singh, Characteristics of the new multiple rogue wave solutions to the fractional generalized CBS-BK equation, Journal of Advanced Research, 38 (2022), 131–142.
  • [48] R. F. Zinati and J. Manafian, Applications of He’s semi-inverse method, ITEM and GGM to the Davey-Stewartson equation, The european physical journal plus, 132 (2017), 1–26.
آمار
تعداد مشاهده مقاله: 513
تعداد دریافت فایل اصل مقاله: 515


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب