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Abdullayev, Ilyos, Akhmetshin, Elvir, Krasnovskiy, Evgeny, Tuguz, Nalbiy, Mashentseva, Galina. (1403). Soliton solutions to the DS and generalized DS system via an analytical method. سامانه مدیریت نشریات علمی, 13(1), 233-248. doi: 10.22034/cmde.2024.60337.2576
Ilyos Sultanovich Abdullayev; Elvir Munirovich Akhmetshin; Evgeny Efimovich Krasnovskiy; Nalbiy Salikhovich Tuguz; Galina Mashentseva. "Soliton solutions to the DS and generalized DS system via an analytical method". سامانه مدیریت نشریات علمی, 13, 1, 1403, 233-248. doi: 10.22034/cmde.2024.60337.2576
Abdullayev, Ilyos, Akhmetshin, Elvir, Krasnovskiy, Evgeny, Tuguz, Nalbiy, Mashentseva, Galina. (1403). 'Soliton solutions to the DS and generalized DS system via an analytical method', سامانه مدیریت نشریات علمی, 13(1), pp. 233-248. doi: 10.22034/cmde.2024.60337.2576
Abdullayev, Ilyos, Akhmetshin, Elvir, Krasnovskiy, Evgeny, Tuguz, Nalbiy, Mashentseva, Galina. Soliton solutions to the DS and generalized DS system via an analytical method. سامانه مدیریت نشریات علمی, 1403; 13(1): 233-248. doi: 10.22034/cmde.2024.60337.2576

Soliton solutions to the DS and generalized DS system via an analytical method

Computational Methods for Differential Equations
مقاله 17، دوره 13، شماره 1، فروردین 2025، صفحه 233-248    اصل مقاله (1.18 M)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.60337.2576
نویسندگان
Ilyos Sultanovich Abdullayev* 1؛ Elvir Munirovich Akhmetshin2؛ Evgeny Efimovich Krasnovskiy3؛ Nalbiy Salikhovich Tuguz4؛ Galina Mashentseva5
1Department of Management and Marketing, Faculty of Social and Economic Sciences, Urgench State University, Urgench, 220100, Uzbekistan.
2Department of Economics and Management, Faculty of Economic and Legal Sciences Kazan Federal University, Elabuga Institute of KFU, 423604, Elabuga, Russian Federation, Republic of Tatarstan.
3Department of Applied Mathematics, Bauman Moscow State Technical University, Russian Federation.
4Department of Higher Mathematics, Kuban State Agrarian University named after I.T. Trubilin, Krasnodar region, 350044, Russian Federation.
5Department of Economics and Humanities, Faculty of Higher Education Kamyshin Technological Institute (branch of) Volgograd State Technical University, Russian Federation.
چکیده
In this article, the exact solutions for nonlinear Drinfeld-Sokolov (DS) and generalized Drinfeld-Sokolov (gDS) equations are established. The rational Exp-function method (EFM) is used to construct solitary and soliton solutions of nonlinear evolution equations. This method is developed for searching exact traveling wave solutions of nonlinear partial differential equations. Also, exact solutions with solitons and periodic structures are obtained. The obtained results are not only presented numerically but are also accompanied by insightful physical interpretations, enhancing the understanding of the complex dynamics described by these mathematical models. The utilization of the rational EFM and the broad spectrum of obtained solutions contribute to the depth and significance of this research in the field of nonlinear wave equations.
کلیدواژه‌ها
Exp–function method؛ Nonlinear partial differential equation؛ Drinfeld-Sokolov system؛ Generalized Drinfeld-Sokolov؛ Solitons and periodic structures؛ Traveling wave solution
مراجع
  • [1] M. A. Abdou, Generalized solitonary and periodic solutions for nonlinear partial differential equations by the Exp–function method, Nonlinear Dyn, 52 (2008), 1–9.
  • [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. Bekir, Applications of the extended tanh method for coupled nonlinear evolution equations, Commun. Nonlin. Sci. Numer. Simul, 13 (2008), 1748–1757.
  • [4] A. Boz and A. Bekir, Application of Exp–function method for (3+1)-dimensional nonlinear evolution equations, Comput. Math. Appl, 56 (2008), 1451–1456.
  • [5] M. Dehghan and J. Manafian, The solution of the variable coefficients fourth–order parabolic partial differential equations by homotopy perturbation method, Z. Naturforsch, 64(a) (2009), 420-430.
  • [6] 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), 448-479.
  • [7] 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.
  • [8] 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.
  • [9] M. Dehghan, J. Manafian Heris, 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 for Heat Fluid Flow, 21 (2011), 736-753.
  • [10] M. Dehghan, J. Manafian Heris, and A. Saadatmandi, Analytical treatment of some partial differential equations arising in mathematical physics by using the Exp-function method, Int. J. Modern Phys. B, 25 (2011), 2965-2981.
  • [11] M. Fazli Aghdaei and J. Manafianheris, Exact solutions of the couple Boiti-Leon-Pempinelli system by the generalized (GG0 )-expansion method, J. Math. Extension, 5 (2011), 91-104.
  • [12] AP. Fordy, Soliton theory: a survey of results, Manchester: MUP, 1990.
  • [13] U. Goktas and E. Hereman, Symbolic computation of conserved densities for systems of nonlinear evolution equations, J. Symb. Comput, 24 (1997), 591-622.
  • [14] 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.
  • [15] J. H. He, Non-perturbative method for strongly nonlinear problems. Dissertation, De-Verlag im Internet GmbH, Berlin, (2006).
  • [16] J. H. He and X. H. Wu, Exp–function method for nonlinear wave equations, Chaos, Solitons Fractals, 30 (2006), 700-708.
  • [17] J. H. He, S. K. Elagan, and Z. B. Li, Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus, Phys. Lett. A, 376 (2012), 257-259.
  • [18] R. Hirota, The Direct Method in Soliton Theory, Cambridge Univ. Press, 2004.
  • [19] A. J. M. Jawad, M. D. Petkovic, and A. Biswas, Modified simple equation method for nonlinear evolution equations, Appl. Math. Comput., 217 (2010), 869-877.
  • [20] Y. Kivshar and D. Pelinovsky, Self-focusing and transverse instabilities of solitary waves, Phys. Rep, 331 (2000), 117-195.
  • [21] 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.
  • [22] W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys, 60 (1992), 650-654.
  • [23] W. Malfliet and W. Hereman, The tanh method: II. Perturbation technique for conservative systems, Phys. Scr, 54 (1996), 569-575.
  • [24] 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.
  • [25] J. Manafian Heris and M. Lakestani, Solitary wave and periodic wave solutions for variants of the KdV-Burger and the K(n, n)-Burger equations by the generalized tanh-coth method, Commun. Num. Anal., 2013 (2013), 1-18.
  • [26] J. Manafian Heris and M. Lakestani, Exact solutions for the integrable sixth-order Drinfeld-Sokolov-SatsumaHirota system by the analytical methods, International Scholarly Research Notices, 2014 (2014), Article ID 840689, 1-8.
  • [27] 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.
  • [28] 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.
  • [29] 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.
  • [30] 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.
  • [31] 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.
  • [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 Diff. Eq. 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] H. Naher and F. A. Abdullah, New approach of (G’/G)-expansion method and new approach of generalized
  • (G’/G)-expansion method for nonlinear evolution equation, AIP Advan., 3 (2013), 032116, [36] S. Novikov, S. Manakov, L. Pitaevskii, and V. Zakharov, Theory of solitons, NY: Plenum, 1984.
  • [37] P. Olver, Applications of lie groups to differential equations, New York, Springer, 1993.
  • [38] M. Wadati, Introduction to solitons, Pramana: J. Phys, 57 (2001), 841-847.
  • [39] J. Wang, A list of 1 + 1 dimensional integrable equations and their properties, J. Nonlinear Math Phys, 9 (2002), 213-233.
  • [40] A. M. Wazwaz, An analytic study of compactons structures in a class of nonlinear dispersive equations, Math. Comput. Simu, 63 (2003), 35-44.
  • [41] A. M. Wazwaz, Exact and explicit traveling wave solutions for the nonlinear Drinfeld-Sokolov system, Commun. Nonlin. Sci. Numer. Simul, 11 (2006), 311-325.
  • [42] 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.
  • [43] X. H. Wu and J. H. He, Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method, Comput. Math. Appl, 54 (2007), 966-986.
  • [44] N. Zabusky and M. Kruskal, Interaction of solitons in a collisionless plasma and the recurrence of initial states, Phys. Rev. Lett, 15 (1965), 240-243.
  • [45] 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.
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