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

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Hedli, Riadh, Berrimi, Fella. (1405). Comprehensive analysis of three seventh-order KdV-type equations. سامانه مدیریت نشریات علمی, 14(4), 1595-1612. doi: 10.22034/cmde.2025.66573.3121
Riadh Hedli; Fella Berrimi. "Comprehensive analysis of three seventh-order KdV-type equations". سامانه مدیریت نشریات علمی, 14, 4, 1405, 1595-1612. doi: 10.22034/cmde.2025.66573.3121
Hedli, Riadh, Berrimi, Fella. (1405). 'Comprehensive analysis of three seventh-order KdV-type equations', سامانه مدیریت نشریات علمی, 14(4), pp. 1595-1612. doi: 10.22034/cmde.2025.66573.3121
Hedli, Riadh, Berrimi, Fella. Comprehensive analysis of three seventh-order KdV-type equations. سامانه مدیریت نشریات علمی, 1405; 14(4): 1595-1612. doi: 10.22034/cmde.2025.66573.3121

Comprehensive analysis of three seventh-order KdV-type equations

Computational Methods for Differential Equations
مقاله 5، دوره 14، شماره 4، دی 2026، صفحه 1595-1612    اصل مقاله (901.08 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.66573.3121
نویسندگان
Riadh Hedli* 1؛ Fella Berrimi2
1LMFN Laboratory, Mathematics Department, Ferhat Abbas university-Setif 1, Algeria.
2LRSD Laboratory, Computer Science Department, Ferhat Abbas university-Setif 1, Algeria.
چکیده
In this paper, we employ the generalized $\exp(-\psi({\xi}))$-expansion approach to derive analytical solutions for three specific cases of the generalized seventh-order KdV equation: the seventh-order Sawada-Kotera-Ito equation, the seventh-order Lax equation, and the seventh-order Kaup-Kupershmidt equation. These equations hold significant importance in the nonlinear sciences. By utilizing this approach, we obtain a variety of new exact traveling wave solutions for the aforementioned nonlinear models. Moreover, we showcase 2D and 3D contour plots and density plots to acquire comprehensive representations, using cutting-edge scientific instruments. Our results confirm the effectiveness and practicality of the proposed method in solving the aforementioned problems, as well as other nonlinear evolution equations encountered in the domains of engineering and mathematical physics.
کلیدواژه‌ها
Generalized $\exp(-\psi(\xi ))$-expansion method؛ gsKdV equation؛ Nonlinear evolution equation؛ Traveling wave solution؛ Bright soliton solution
مراجع
  • [1] G. Akram, M. Sadaf, S. Arshed, and U. Ejaz, Travelling wave solutions and modulation instability analysis of the nonlinear Manakov-system, J Taibah Univ Sci, 17(1) (2023), 2201967.
  • [2] M. Y. Ali, M. G. Hafez, M. K. H. Chowdury, and M. T. Akter, Analytical and traveling wave solutions to the fifth-order standard Sawada-Kotera equation via the generalized exp( ϕ(ξ))-expansion method, J. Appl. Math. Phys., 4(2) (2016), 262–271.
  • [3] N. H. Aljahdaly, A. R. Seadawy, and W. A. Albarakati, Applications of dispersive analytical wave solutions of nonlinear seventh order Lax and Kaup-Kupershmidt dynamical wave equations, Results Phys., 14 (2019), 102372.
  • [4] M. T. Darvishi, S. Kheybari, and F. Khani, A numerical solution of the Lax’s 7th-order KdV equation by pseu-dospectral method and Darvishi’s preconditioning, Int. J. Contemp. Math. Sciences, 2 (2007), 1097–1106.
  • [5] F. Ferdous, M. Hafez, A. Biswas, M. Ekici, Q. Zhou, M. Alfiras, S. P. Moshokoa, and M. Belic, Oblique reso-nant optical solitons with Kerr and parabolic law nonlinearities and fractional temporal evolution by generalized exp( ϕ(ξ))-expansion, Optik, 178 (2019), 439–448.
  • [6] D. D. Ganji, M. Safari, and R. Ghayor, Application of He’s variational iteration method and Adomian’s decompo-sition method to Sawada–Kotera–Ito seventh-order equation, Numer. Methods Partial Differ. Equ., 27(4) (2011), 887–897.
  • [7] M. Ghasemi, A. Azizi, and M. Fardi, Numerical solution of seven-order Sawada-Kotara equations by homotopy perturbation method, Math. Scientific J., 7(1) (2013), 69–77.
  • [8] M. G. Hafez and D. Lu, Traveling wave solutions for space-time fractional nonlinear evolution equations, Technical Report, (2015), arXiv:1512.00715.
  • [9] R. Hedli and F. Berrimi, Novel traveling wave solutions of generalized seventh-order KdV equation and related equation, Comput. Methods Differ. Equ., 12(2) (2024), 392–412.
  • [10] R. Hedli and A. Kadem, Exact traveling wave solutions to the fifth-order KdV equation using the exponential expansion method, IAENG Int. J. Appl. Math., 50(1) (2020), 121–126.
  • [11] M. Kumar and A. S. Saxena, New iterative method for solving higher order KdV equations, Int. j. Adv. Res. Sci. Eng., 5(5) (2016), 296–307.
  • [12] M. Lakestani, Numerical solutions of the KdV equation using B-spline functions, Iran J Sci Technol Trans Sci,41(2) (2017), 409–417.
  • [13] D. Lu, C. Yue, and M. Arshad, Traveling wave solutions of space-time fractional generalized fifth-order KdV equation, Adv. Math. Phys., 2017 (2017), e6743276.
  • [14] 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 Differ. Equ. Appl. Math., 9 (2024), 100600.
  • [15] M. M. Miah, H. M. S. Ali, M. A. Akbar, and A. R. Seadawy, New applications of the two-variable (G′/G, 1/G)-expansion method for closed-form traveling wave solutions of integro-differential equations, J. Ocean Eng. Sci., 4(2) (2019), 132–143.
  • [16] N. Raza, J. Afzal, A. Bekir, and H. Rezazadeh, Improved tan(ϕ(ξ)/2)-expansion approach for Burgers equation in nonlinear dynamical model of ion acoustic waves, Braz. J. Phys., 50(3) (2020), 254–262.
  • [17] H. Rezazadeh, J. Vahidi, A. Zafar, and A. Bekir, The functional variable method to find new exact solutions of the nonlinear evolution equations with dual-power-law nonlinearity, Int. J. Nonlinear Sci. Numer. Simul., 21(3-4) (2020), 249–257.
  • [18] A. H. Salas and C. A. Gòmez S, Application of the Cole-Hopf transformation for finding exact solutions to several forms of the seventh-order KdV equation, Math. Probl. Eng., 2010 (2010), e194329.
  • [19] I. Samir, A. H. Arnous, A. M. Elsherbeny, M. Mirzazadeh, M. S. Hashemi, and M. Eslami, Solitary waves with two new nonlocal boussinesq types equations using a couple of integration schemes, Comput. Methods Differ. Equ., 12(4) (2024), 749–762.
  • [20] M. Saravi, A. Nikkar, M. Hermann, and R. Ahari, A new modified approach for solving seven-order Sawada-Kotara equations, J. Math. Comput. Sci., 6(3) (2013), 230–237.
  • [21] Y. Shen and B. Tian, Bilinear auto-Bäcklund transformations and soliton solutions of a (3+1)-dimensional generalized nonlinear evolution equation for the shallow water waves, Appl. Math. Lett., 122 (2021), 107301.
  • [22] G. U. Urazboev, I. I. Baltaeva, and I. D. Rakhimov, The generalized (G′/G)-expansion method for the loaded Korteweg–de Vries equation, J. Appl. Ind. Math., 15(4) (2021), 679–685.
  • [23] A. M. Wazwaz, The Hirota’s direct method and the tanh–coth method for multiple-soliton solutions of the Sawada–Kotera–Ito seventh-order equation, Appl. Math. Comput., 199(1) (2008), 133–138.
  • [24] X. H. Wu, Y. T. Gao, X. Yu, and F. Y. Liu, Generalized Darboux transformation and solitons for a Kraenkel-Manna-Merle system in a ferromagnetic saturator, Nonlinear Dyn, 111(15) (2023), 14421–14433.
  • [25] L. Zada, R. Nawaz, M. Ayaz, H. Ahmad, H. Alrabaiah, and Y. M. Chu, New algorithm for the approximate solution of generalized seventh order Korteweg-Devries equation arising in shallow water waves, Results Phys., 20 (2021), 103744.
  • [26] T. Y. Zhou, B. Tian, Y. Shen, and X. T. Gao, Bilinear form, bilinear auto-Bäcklund transformation, soliton and half-periodic kink solutions on the non-zero background of a (3+1)-dimensional time-dependent-coefficient Boiti-Leon-Manna-Pempinelli equation, Wave Motion, 121 (2023), 103180.
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