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

 آمار

تعداد نشریات45
تعداد شماره‌ها1,530
تعداد مقالات18,634
تعداد مشاهده مقاله61,230,639
تعداد دریافت فایل اصل مقاله22,020,548
Telezhko, Irina, Dengaev, Alexey, Iarkhamova, Alfiia, Revyakina, Elena, Kolcova, Nadezhda. (1403). On analytical solutions of the ZK equation and related equations by using the generalized ( G′/G )-expansion method. سامانه مدیریت نشریات علمی, 13(1), 258-270. doi: 10.22034/cmde.2024.61348.2635
Irina Telezhko; Alexey Dengaev; Alfiia Iarkhamova; Elena Revyakina; Nadezhda Kolcova. "On analytical solutions of the ZK equation and related equations by using the generalized ( G′/G )-expansion method". سامانه مدیریت نشریات علمی, 13, 1, 1403, 258-270. doi: 10.22034/cmde.2024.61348.2635
Telezhko, Irina, Dengaev, Alexey, Iarkhamova, Alfiia, Revyakina, Elena, Kolcova, Nadezhda. (1403). 'On analytical solutions of the ZK equation and related equations by using the generalized ( G′/G )-expansion method', سامانه مدیریت نشریات علمی, 13(1), pp. 258-270. doi: 10.22034/cmde.2024.61348.2635
Telezhko, Irina, Dengaev, Alexey, Iarkhamova, Alfiia, Revyakina, Elena, Kolcova, Nadezhda. On analytical solutions of the ZK equation and related equations by using the generalized ( G′/G )-expansion method. سامانه مدیریت نشریات علمی, 1403; 13(1): 258-270. doi: 10.22034/cmde.2024.61348.2635

On analytical solutions of the ZK equation and related equations by using the generalized ( G′/G )-expansion method

Computational Methods for Differential Equations
مقاله 19، دوره 13، شماره 1، فروردین 2025، صفحه 258-270    اصل مقاله (380 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.61348.2635
نویسندگان
Irina Telezhko* 1؛ Alexey Dengaev2؛ Alfiia Iarkhamova3؛ Elena Revyakina4؛ Nadezhda Kolcova5
1Peoples' Friendship University of Russia (RUDN University), Moscow, Russia.
2Gubkin Russian State University of Oil and Gas, Moscow, Russia.
3Kazan Federal University, Kazan, Russia.
4Don State Technical University, Rostov-on-Don, Russia.
5Kuban State University, Krasnodar, Russia.
چکیده
The generalized ( G′/G )-expansion method with the aid of Maple is proposed to seek exact solutions of nonlinear evolution equations. For finding exact solutions are expressed three types of solutions that include hyperbolic function solution, trigonometric function solution, and rational solution. The article studies the Zakharov–Kuznetsov (ZK) equation, the generalized ZK (gZK) equation, and the generalized forms of these equations. Exact solutions with traveling wave solutions of nonlinear evolution equations are obtained. It is shown that the proposed method is direct, effective and can be used for many other nonlinear evolution equations.
کلیدواژه‌ها
Generalized ( G′/G )-expansion method؛ Zakharov–Kuznetsov equation؛ Generalized Zakharov-Kuznetsov equation؛ Traveling wave solution
مراجع
  • [1] M. J. Ablowitz and P. A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering, Cambridge: Cambridge University Press, 1991.
  • [2] N. H. Ali, S. A. Mohammed, and J. Manafian, Study on the simplified MCH equation and the combined KdVmKdV equations with solitary wave solutions, Partial Diff. Eq. Appl. Math., 9 (2024), 100599.
  • [3] A. Barari, H. D. Kaliji, M. Ghadimi, and G. Domairry, Nonlinear vibration of Euler-Bernoulli beams, Latin American J. Solids Structures, 8 (2011), 139-148.
  • [4] K. Batiha, Approximate analytical solution for the Zakharov–Kuznetsov equations with fully nonlinear dispersion, J. Comput. Appl. Math, 216 (2008), 157-163.
  • [5] A. Bekir, Application of the  -expansion method for nonlinear evolution equations, Phys. Lett. A, 372 (2008), 3400-3406.
  • [6] C. Chun and R. Sakthivel, Homotopy perturbation technique for solving two-point boundary value problems– comparison with other methods, Comput. Phys. Commu, 181 (2010), 1021-1024.
  • [7] M. Dehghan and J. Manafian, The solution of the variable coefficients fourth–order parabolic partial differential equations by homotopy perturbation method, Z. Naturforsch, 64 (2009), 420-430.
  • [8] M. Dehghan, J. Manafian, and A. Saadatmandi, The solution of the linear fractional partial differential equations using the homotopy analysis method, Z. Naturforsch, 65(a) (2010), 935-949.
  • [9] M. Dehghan, J. Manafian, and A. Saadatmandi, Solving nonlinear fractional partial differential equations using the homotopy analysis method, Num. Meth. Partial Differential Eq. J, 26 (2010), 486-498.
  • [10] M. Dehghan, J. Manafian, and A. Saadatmandi, Application of semi–analytic methods for the Fitzhugh–Nagumo equation, which models the transmission of nerve impulses, Math. Meth. Appl. Sci, 33 (2010), 1384-1398.
  • [11] M. Dehghan and J. Manafian, Study of the wave-breaking’s qualitative behavior of the Fornberg-Whitham equation via quasi-numeric approaches, Int. J. Num. Methods Heat Fluid Flow, to appear in 2011.
  • [12] M. Dehghan, J. Manafian, and A. Saadatmandi, Application of the Exp-function method for solving a partial differential equation arising in biology and population genetics, Int. J. Num. Methods Heat and Fluid Flow, 21 (2011), 736-753.
  • [13] M. Dehghan, J. Manafian, and A. Saadatmandi, Analytical treatment of some partial differential equations arising in mathematical physics by using the Exp-function method, Int. J. Modern Physics, B, 25 (2011), 2965-2981.
  • [14] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A, 277 (2000), 212-218.
  • [15] F. Farrokhzad, P. Mowlaee, A. Barari, A. J. Choobbasti, and H. D. Kaliji, Analytical investigation of beam deformation equation using perturbation, homotopy perturbation, variational iteration and optimal homotopy asymptotic methods, Carpathian J, Math, 27 (2011), 51-63.
  • [16] M. Ghadimi, H. D. Kaliji, and A. Barari, Analytical Solutions to Nonlinear Mechanical Oscillation Problems, J. Vibroengineering, 13 (2011), 133-143.
  • [17] H. Gao and R.X. Zhao, New application of the  -expansion method to higher-order nonlinear equations, Appl. Math. Comput, 215 (2009), 2781–2786.
  • [18] Y. Gu, S. Malmir, J. Manafian, O. A. Ilhan, A. 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 Phys., 43 (2022), 106032.
  • [19] J. H. He, Variational iteration method a kind of non-linear analytical technique: some examples, Int. J. Nonlinear Mech, 34 (1999), 699-708.
  • [20] J. H. He and X. H. Wu, Exp–function method for nonlinear wave equations, Chaos, Solitons Fractals, 30 (2006), 700-708.
  • [21] R. Hirota, The Direct Method in Soliton Theory, Cambridge Univ., Press, 2004.
  • [22] W. Huang, A polynomial expansion method and its application in the coupled Zakharov–Kuznetsov equations, Chaos, Solitons Fractals, 29 (2006), 365-371.
  • [23] M. Inc, Exact solutions with solitary patterns for the Zakharov–Kuznetsov equations with fully nonlinear dispersion, Chaos Solitons Fractals, 33 (2007), 1783-1790.
  • [24] A. Khajeh, A. Yousefi-Koma, M. Vahdat, and M. M. Kabir, Exact traveling wave solutions for some nonlinear equations arising in biology and engineering, World Appl. Sci. J, 9 (2010), 1433-1442.
  • [25] H. D. Kaliji, A. Fereidoon, M. Ghadimi, and M. Eftari, Analytical Solutions for Investigating Free Vibration of Cantilever Beams, World Appl. Sci. J. (Special Issue of Applied Math), 9 (2010), 44-48.
  • [26] M. Lakestani, J. Manafian, A. R. Najafizadeh, and M. Partohaghighi, Some new soliton solutions for the nonlinear the fifth-order integrable equations, Comput. Meth. Diff. Equ., 10(2) (2022), 445-460.
  • [27] J. Manafian Heris and M. Bagheri, Exact Solutions for the Modified KdV and the Generalized KdV Equations via Exp-Function Method, J. Math. Extension, 4 (2010), 77-98.
  • [28] 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.
  • [29] 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.
  • [30] 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.
  • [31] 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, J. Geom. Phys., 150 (2020), 103598.
  • [32] 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.
  • [33] X. H. Menga, W. J. Liua, H. W. Zhua, C. Y. Zhang, and B. Tian, Multi-soliton solutions and a B¨acklund transformation for a generalized variable-coefficient higher-order nonlinear Schr¨o dinger equation with symbolic computation, Phys. A, 387 (2008), 97-107.
  • [34] S. R. Moosavi, N. Taghizadeh, and J. Manafian, Analytical approximations of one-dimensional hyperbolic equation with non-local integral conditions by reduced differential transform method, Comput. Meth. Diff. Equ., 8(3) (2020), 537-552.
  • [35] M. H .M. Moussa, Similarity solutions to non-linear partial differential equation of physical phenomena represented by the Zakharov-Koznetsov equation, Int. J. Eng. Sci, 39 (2001), 1565-1575.
  • [36] Y. Z. Peng, Exact traveling wave solutions for the Zakharov–Kuznetsov equation, Appl. Math. Comput, 199 (2008), 397-405.
  • [37] A. Sousaraie and Z. Bagheri, Traveling wave solution for nonlinear Klein-Gordon equation, World Appl. Sci. J, 11 (2010), 367–370.
  • [38] B. K. Shivamoggi, The Painleve´ analysis of the Zakharov–Kuznetsov equation, Phys. Scr, 42 (1990), 641-642.
  • [39] M. Wang, X. Li, and J. Zhang, The  -expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A, 372 (2008), 417-423.
  • [40] A. M. Wazwaz, Exact solutions with solitons and periodic structures for the Zakharov–Kuznetsov equation and its modified form, Commu. Nonlinear Sci. Num. Simu, 161 (2005), 577-590.
  • [41] A. M. Wazwaz, Traveling wave solutions for combined and double combined sine-cosine-Gordon equations by the variable separated ODE method, Appl. Math. Comput, 177 (2006), 755-760.
  • [42] A. M. Wazwaz, The extended tanh method for the Zakharov-Kuznetsov (ZK) equation, the modified ZK equation, and its generalized forms, Commu. Nonlinear Sci. Num. Simu, 13 (2008), 1039-1047.
  • [43] E. M. E. Zayed and A. Khaled Gepreel, Some applications of the  -expansion method to non-linear partial differential equations, Appl. Math. Comput, 212 (2009), 1–13.
  • [44] V. E. Zakharov and E. A. Kuznetsov, On three–dimensional solitons, Sov. Phys, 39 (1974), 285-288.
  • [45] S. Zhang, J. L. Tong, and W. Wang, A generalized  -expansion method for the mKdV equation with variable coefficients, Phys. Lett. A, 372 (2008), 2254-2257.
  • [46] J. Zhang,, X. Wei, and Y. Lu, A generalized  -expansion method and its applications, Phys. Lett. A, 372 (2008), 3653-3658.
  • [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, J. Adv. Res., 38 (2022), 131-142.
  • [48] X. Zhao, H. Zhou, Y. Tang, and H. Jia, Traveling wave solutions for modified Zakharov–Kuznetsov equation, Appl. Math. Comput, 181 (2006), 634-648.
آمار
تعداد مشاهده مقاله: 463
تعداد دریافت فایل اصل مقاله: 449


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب