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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. (1402). Novel traveling wave solutions of generalized seventh-order KdV equation and related equation. سامانه مدیریت نشریات علمی, 12(2), 392-412. doi: 10.22034/cmde.2023.53478.2254
Riadh Hedli; Fella Berrimi. "Novel traveling wave solutions of generalized seventh-order KdV equation and related equation". سامانه مدیریت نشریات علمی, 12, 2, 1402, 392-412. doi: 10.22034/cmde.2023.53478.2254
Hedli, Riadh, Berrimi, Fella. (1402). 'Novel traveling wave solutions of generalized seventh-order KdV equation and related equation', سامانه مدیریت نشریات علمی, 12(2), pp. 392-412. doi: 10.22034/cmde.2023.53478.2254
Hedli, Riadh, Berrimi, Fella. Novel traveling wave solutions of generalized seventh-order KdV equation and related equation. سامانه مدیریت نشریات علمی, 1402; 12(2): 392-412. doi: 10.22034/cmde.2023.53478.2254

Novel traveling wave solutions of generalized seventh-order KdV equation and related equation

Computational Methods for Differential Equations
مقاله 14، دوره 12، شماره 2، خرداد 2024، صفحه 392-412    اصل مقاله (806.34 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.53478.2254
نویسندگان
Riadh Hedli* 1؛ Fella Berrimi2
1Department of Mathematics Faculty of Sciences University of Ferhat Abbas Setif 1 Algeria.
2Department of Computer Science Faculty of Sciences University of Ferhat Abbas Setif 1 Algeria.
چکیده
In this paper, we acquire novel traveling wave solutions of the generalized seventh-order Korteweg–de Vries equation and the seventh-order Kawahara equation as a special case with physical interest. Primarily, we use the advanced $\exp (-\varphi (\xi ))$-expansion method to find new exact solutions of the first equation, by considering two auxiliary equations. Then, we attain some exact solutions of the seventh-order Kawahara equation by using this method with another auxiliary equation, and also using the modified $(G^{'}/G) $-expansion method, where G satisfies a second-order linear ordinary differential equation. Additionally, utilizing the recent scientific instruments, the 2D, 3D, and contour plots are displayed. The solutions obtained in this paper include bright solitons, dark solitary wave solutions, and multiple dark solitary wave solutions. It is shown that these two methods provide an effective mathematical tool for solving nonlinear evolution equations arising in mathematical physics and engineering.
کلیدواژه‌ها
Nonlinear evolution equation؛ Generalized seventh-order Korteweg-de Vries equation؛ Traveling wave solution؛ $\exp (-\varphi (\xi ))$-expansion method؛ $(G^{'}/G) $-expansion method
مراجع
  • [1] M. N. Alam and X. Li, Exact traveling wave solutions to higher order nonlinear equations, J. Ocean Eng. Sci., 4(3) (2019), 276–288.
  • [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, Some applications of the modified (G0/G2)-expansion method in mathematical physics, Results Phys., 13 (2019), 102272.
  • [4] H. Alotaibi, Explore Optical Solitary Wave Solutions of the KP Equation by Recent Approaches, Crystals, 12(2) (2022), 159.
  • [5] N. A. Alzaid and B. A. Alrayiqi, Approximate solution method of the seventh order KdV equations by decomposition method, J. Appl. Math. Phys., 7 (2019), 2148–2155.
  • [6] M. Areshi, A. Khan, R. Shah, and K. Nonlaopon, Analytical investigation of fractional-order Newell-WhiteheadSegel equations via a novel transform, AIMS Mathematics, 7(4) (2022), 6936–6958.
  • [7] M. Arshad, A. R. Seadawy, and D. Lu, Study of soliton solutions of higher-order nonlinear Schr¨odinger dynamical model with derivative non-Kerr nonlinear terms and modulation instability analysis, Results Phys., 13 (2019), 102305.
  • [8] S. S. Band, I. Al-Shourbaji, H. Karami, S. Karimi, J. Esfandiari, and A. Mosavi, Combination of group method of data handling (GMDH) and computational fluid dynamics (CFD) for prediction of velocity in channel intake, Appl. Sci., 10(21) (2020), 7521.
  • [9] A. Chauhan and R. Arora, Some exact solutions of (1+1)-dimensional Kaup-system and seventh-order Kawahara equation, Malaya J. Math., 8(1) (2020), 151–158.
  • [10] B. R. Duffy and E. J. Parkes, Travelling solitary wave solutions to a seventh-order generalized KdV equation, Phys. Lett. A, 214(5–6) (1996), 271–272.
  • [11] F. Ferdous, M. G. Hafez, and M. Y. Ali, Obliquely propagating wave solutions to conformable time fractional extended Zakharov–Kuzetsov equation via the generalized exp(−Φ(ξ))-expansion method, SeMA J., 76 (2018), 109–122.
  • [12] F. Ferdous, M. G. Hafez, A. Biswas, M. Ekici, Q. Zhou, M. Alfiras, S. P. Moshokoa, and M. Belic, Oblique resonant optical solitons with Kerr and parabolic law nonlinearities and fractional temporal evolution by generalized exp(−Φ(ξ))-expansion, Optik, 178 (2019), 439–448.
  • [13] Foyjonnesa, N. H. M. Shahen, and M. M. Rahman, Dispersive solitary wave structures with MI Analysis to the unidirectional DGH equation via the unified method, Partial Differ. Equ. Appl. Math., 6 (2022), 100444.
  • [14] B. Ghanbari and K. S. Nisar, Determining new soliton solutions for a generalized nonlinear evolution equation using an effective analytical method, Ain Shams Eng. J., 59(5) (2020), 3171–3179.
  • [15] M. G. Hafez and M. A. Akbar, An exponential expansion method and its application to the strain wave equation in microstructured solids, Ain Shams Eng. J., 6(2) (2015), 683–690.
  • [16] M. G. Hafez and D. Lu, Traveling wave solutions for space-time fractional nonlinear evolution equations, (2015), 17 pages. http://arxiv.org/abs/1512.00715
  • [17] 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.
  • [18] O. A. Ilhan, A. Esen, H. Bulut, and H. M. Baskonus, Singular solitons in the pseudo-parabolic model arising in nonlinear surface waves, Results Phys., 12 (2019), 1712–1715.
  • [19] A. Irshad, S.T. Mohyud-Din, N. Ahmed, and U. Khan, A new modification in simple equation method and its applications on nonlinear equations of physical nature, Results Phys., 7 (2017), 4232–4240.
  • [20] S. Kaewta, S. Sirisubtaweee,S. Koonprasert, and S. Sungnul, Applications of the (G0/G2)-expansion method for solving certain nonlinear conformable evolution equations, Fractal Fract., 5(3) (2021), 8.
  • [21] U. Khan, A. Irshad, N. Ahmed, and S. T. Mohyud-Din, Improved tan -expansion method for (2 + 1)dimensional KP–BBM wave equation, Opt. Quant. Electron., 50 (2018), 135.
  •  [22] N. A. Kudryashov, The Painlev´e approach for finding solitary wave solutions of nonlinear nonintegrable differential equations, Optik, 183 (2019), 642–649.
  • [23] V. S. Kumar, H. Rezazadeh, M. Eslami, F. Izadi, and M. S. Osman, Jacobi elliptic function expansion method for solving KdV equation with conformable derivative and dual-power law nonlinearity, Int. J. Appl. Comput. Math., 5 (2019), 127.
  • [24] M. Lakestani, J. Manafian, A. R. Najafizadeh, and M. Partohaghighi, Some new soliton solutions for the nonlinear the fifth-order integrable equations, Comput. Methods Differ. Equ., 10 (2) (2022), 445–460.
  • [25] Z. Li, T. Han, and C. Huang, Bifurcation and new exact traveling wave solutions for time-space fractional Phi-4 equation, AIP Advances, 10 (2020), 115113.
  • [26] D. Lu and M. Ye, Traveling wave solutions for the nonlinear fractional Sharma-Tasso-Olever equation, Int. J. Math. Res., 6(1) (2017), 36–45.
  • [27] D. Lu, C. Yue, and M. Arshad, Traveling wave solutions of space-time fractional generalized fifth-order KdV equation, Adv. Math. Phys., (2017), 6743276, 6 pages.
  • [28] W. Ma, Travelling wave solutions to a seventh-order generalized KdV equation, Phys. Lett. A, 180(3) (1993), 221–224.
  • [29] J. Manafian, Optical solitons in a power-law media with fourth order dispersion by three integration methods, Cogent math. stat., 5(1) (2018), 1434924.
  • [30] S. C. Mancas and W. A. Hereman, Traveling wave solutions to fifth- and seventh-order Korteweg–de Vries equations: Sech and Cn solutions, J. Phys. Soc. Japan., 87 (2018), 114002.
  • [31] M. Mirzazadeh, M. Eslami, and A. H. Arnous, Dark optical solitons of Biswas-Milovic equation with dual-power law nonlinearity, Eur. Phys. J. Plus, 130(4) (2015), 114002.
  • [32] S. T. Mohyud-Din, M. A. Noor, and K. I. Noor, Traveling wave solutions of seventh-order generalized KdV equations using He’s polynomials, Int. J. Nonlinear Sci. Numer. Simul., 10(2) (2009), 227–233.
  • [33] A. Molajou, V. Nourani, A. Afshar, M. Khosravi, and A. Brysiewicz, Optimal design and feature selection by genetic algorithm for emotional artificial neural network (EANN) in Rainfall-Runoff modeling, Water Resour. Manage., 35 (2021), 2369–2384.
  • [34] E. J. Parkes, Z. Zhu, B. R. Duffy, and H. Huang, Sech-polynomial travelling solitary-wave solutions of odd-order generalized KdV equations, Phys. Lett. A, 248(2–4) (1998), 219–224.
  • [35] Y. Pomeau, A. Ramani, and B. Grammaticos, Structural stability of the Korteweg-de Vries solitons under a singular perturbation, Physica D, 31(1) (1988), 127–134.
  • [36] S. Sahoo and S. Saha Ray, Solitary wave solutions for time fractional third order modified KdV equation using two reliable techniques (G /G)-expansion method and improved (G /G)-expansion method, Physica A, 448(15) (2016), 265–282.
  • [37] A. Samil and A. Tugba, Comparison between the (G /G)-expansion method and the modified extended tanh method, Open Phys., 14(1) (2016), 88–94.
  • [38] A. R. Seadawy, D. Yaro, and D. Lu, Propagation of nonlinear waves with a weak dispersion via coupled (2+1)dimensional Konopelchenko–Dubrovsky dynamical equation, Pramana – J. Phys., 94 (2020), 17.
  • [39] M. Wang, X. Li, and J. Zhang, The -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A, 372 (2008), 417–423.
  • [40] A. M. Wazwaz, Soliton solutions for seventh-order Kawahara equation with time-dependent coefficients, Mod. Phys. Lett. B, 25 (2011), 643–648.
  • [41] A. M. Wazwaz, The simplified Hirota’s method for studying three extended higher-order KdV-type equations, J. Ocean Eng. Sci., 1 (2016), 181–185.
  • [42] L. Wu , X. Zhang, and J. Manafian, On the exact solitary wave solutions to the new (2 + 1) and (3 + 1)dimensional extensions of the Benjamin-Ono equations, Adv. Math. Phys., 2021 (2021), ID 6672819.
  • [43] A. Yokus, K. K. Ali, R. Yilmazer, and H. Bulut, On exact solutions of the generalized Pochhammer-Chree equation, Comput. Methods Differ. Equ., 10(3) (2022), 746–754.
  • [44] E. M. E. Zayed and K. A. Gepreel, The modified  -expansion method and its applications to construct exact solutions for nonlinear PDEs, WSEAS Trans. Math., 8(10) (2011), 270–278.
  • [45] M. Zhao and C. Li, The exp(−ϕ(ξ))-expansion method applied to nonlinear evolution equations, (2008), http://www.paper.edu.cn.
  • [46] Q. Zhou, Analytical study of solitons in magneto-electro-elastic circular rod, Nonlinear Dyn., 83 (2016), 1403–1408.
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