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

 آمار

تعداد نشریات45
تعداد شماره‌ها1,550
تعداد مقالات18,890
تعداد مشاهده مقاله63,337,672
تعداد دریافت فایل اصل مقاله23,090,784
Akhmetshin, Elvir, Abdullayev, Ilyos, Makhmudov, Samariddin, Dakhkilgova, Kamila, Korotaeva, Irina, Yanovskaya, Galina. (1405). Application of tanh–coth method for combined and double combined sinh–cosh–Gordon equations arising from chemical reactions to water surface gravity waves. سامانه مدیریت نشریات علمی, 14(3), 1337-1352. doi: 10.22034/cmde.2025.67655.3234
Elvir Akhmetshin; Ilyos Abdullayev; Samariddin Makhmudov; Kamila Dakhkilgova; Irina Korotaeva; Galina Yanovskaya. "Application of tanh–coth method for combined and double combined sinh–cosh–Gordon equations arising from chemical reactions to water surface gravity waves". سامانه مدیریت نشریات علمی, 14, 3, 1405, 1337-1352. doi: 10.22034/cmde.2025.67655.3234
Akhmetshin, Elvir, Abdullayev, Ilyos, Makhmudov, Samariddin, Dakhkilgova, Kamila, Korotaeva, Irina, Yanovskaya, Galina. (1405). 'Application of tanh–coth method for combined and double combined sinh–cosh–Gordon equations arising from chemical reactions to water surface gravity waves', سامانه مدیریت نشریات علمی, 14(3), pp. 1337-1352. doi: 10.22034/cmde.2025.67655.3234
Akhmetshin, Elvir, Abdullayev, Ilyos, Makhmudov, Samariddin, Dakhkilgova, Kamila, Korotaeva, Irina, Yanovskaya, Galina. Application of tanh–coth method for combined and double combined sinh–cosh–Gordon equations arising from chemical reactions to water surface gravity waves. سامانه مدیریت نشریات علمی, 1405; 14(3): 1337-1352. doi: 10.22034/cmde.2025.67655.3234

Application of tanh–coth method for combined and double combined sinh–cosh–Gordon equations arising from chemical reactions to water surface gravity waves

Computational Methods for Differential Equations
مقاله 20، دوره 14، شماره 3، مهر 2026، صفحه 1337-1352    اصل مقاله (468.35 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2025.67655.3234
نویسندگان
Elvir Akhmetshin* 1؛ Ilyos Abdullayev2؛ Samariddin Makhmudov3؛ Kamila Dakhkilgova4؛ Irina Korotaeva5؛ Galina Yanovskaya5
11. Department of Economics, Mamun University, Khiva, Uzbekistan. \\ 2. Faculty of Economics, RUDN University, Moscow, Russia.
2Department of Business and Management, Urgench State University, Urgench, Uzbekistan.
31. Department of Finance and Tourism, Termez University of Economics and Service, Termez, Uzbekistan.\\ 2. Department of Finance, Alfraganus University, Tashkent, Uzbekistan.
4Department of programming and infocommunication technologies, Kadyrov Chechen State University, Grozny, Russia.
5Department I-11 Foreign language for aerospace specialties, Moscow Aviation Institute, Moscow, Russia.
چکیده
An application of the generalized tanh–coth method to search for exact solutions of nonlinear partial differential equations is analyzed. This method is used for the combined and the double combined sinh-cosh-Gordon equations. The generalized tanh–coth method was used to construct periodic wave and solitary wave solutions of nonlinear evolution equations. This method is developed for searching for exact travelling wave solutions of nonlinear partial differential equations. It is shown that the generalized $tanh-coth$ method, with the help of symbolic computation, provides a straightforward and powerful mathematical tool for solving nonlinear problems.
کلیدواژه‌ها
The generalized tanh–coth method؛ The combined and the double combined sinh–cosh–Gordon equations؛ Solitary wave and periodic wave solutions
مراجع
  • [1] M. J. Ablowitz and P. A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering, Cambridge University Press, Cambridge, 1991.
  • [2] S. Z. Ahmedov, R. A. Gasimov, and V. M. Habibov, Solution of the Mixed Problem for the Non-Homogeneous Parabolic Equation with Time Derivative in the Boundary Condition, Adv. Math. Models Appl., (2025).
  • [3] N. H. Ali, S. A. Mohammed, and J. Manafian, New explicit soliton and other solutions of the Van der Waals model through the ESHGEEM and the IEEM, J. Mod. Technol. Eng., 8(1) (2023), 5–18.
  • [4] S. Aliyeva and I. Kerimova, Optimization Principles of Mechanical Transmission of Lifting Devices, J. Mod. Technol. Eng., (2025).
  • [5] B. Ayhan and A. Bekir, The (G)-expansion method for the nonlinear lattice equations, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 3490–3498.
  • [6] M. Bagheri and J. Manafian Heris, Differential transform method for solving the linear and nonlinear West-ervelt equation, J. Math. Ext., 6 (2012), 81–91.
  • [7] A. Bekir, Application of the ( G )-expansion method for nonlinear evolution equations, Phys. Lett. A, 372 (2008), 3400–3406.
  • [8] A. Bekir and A. C. Cevikel, The tanh-coth method combined with the Riccati equation for solving nonlinear coupled equation in mathematical physics, J. King Saud Univ., Sci., 23 (2011), 127–132.
  • [9] L. A. Dawod, M. Lakestani, and J. Manafian, Breather Wave Solutions for the (3+1)-D Generalized Shallow Water Wave Equation with Variable Coefficients, Qual. Theory Dyn. Syst., 22 (2023), 127.
  • [10] M. Dehghan and J. Manafian, The solution of the variable coefficients fourth–order parabolic partial differential equations by homotopy perturbation method, Z. Naturforsch., 64a (2009), 420–430.
  • [11] M. Dehghan, J. Manafian, and A. Saadatmandi, The solution of the linear fractional partial differential equations using the homotopy analysis method, Z. Naturforsch., 65a (2010), 935–949.
  • [12] M. Dehghan, J. Manafian, and A. Saadatmandi, Solving nonlinear fractional partial differential equations using the homotopy analysis method, Numer. Methods Partial Differential Equations, 26 (2010), 448–479.
  • [13] 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. Methods Appl. Sci., 33 (2010), 1384–1398.
  • [14] 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. Numer. Methods Heat Fluid Flow, 21 (2011), 736–753.
  • [15] 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. Mod. Phys. B, 25 (2011), 2965–2981.
  • [16] E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A, 277 (2000), 212–218.
  • [17] M. Fazli Aghdaei and J. Manafianheris, Exact solutions of the couple Boiti-Leon-Pempinelli system by the generalized (G′)-expansion method, J. Math. Ext., 5 (2011), 91–104.
  • [18] B. Feng, J. Manafian, O. A. Ilhan, A. M. Rao, and A. H. Agadi, Cross-kink wave, solitary, dark, and periodic wave solutions by bilinear and He’s variational direct methods for the KP-BBM equation, Int. J. Mod. Phys. B, 35(27) (2021), 2150275.
  • [19] Z. Fu, S. Liu, and S. Liu, Exact solutions to double and triple sinh-Gordon equations, Z. Naturforsch., 59a (2004), 933–937.
  • [20] Y. Gu, J. Manafian, S. Malmir, B. Eslami, and O. A. Ilhan, Lump, lump-trigonometric, breather waves, periodic wave and multi-waves solutions for a Konopelchenko-Dubrovsky equation arising in fluid dynamics, Int. J. Mod. Phys. B, 37(15) (2023), 2350141.
  • [21] J. H. He, Variational iteration method a kind of non-linear analytical technique: some examples, Int. J. Non-Linear Mech., 34 (1999), 699–708.
  • [22] R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, 2004.
  • [23] W. Malfliet, Solitary wave solutions of nonlinear wave equations, Am. J. Phys., 60 (1992), 650–654.
  • [24] W. Malfliet and W. Hereman, The tanh method: II. Perturbation technique for conservative systems, Phys. Scr., 54 (1996), 569–575.
  • [25] W. Malfliet, The tanh method: I. Exact solutions of nonlinear evolution and wave equations, Phys. Scr., 54 (1996), 563–558.
  • [26] J. Manafian Heris and M. Bagheri, Exact solutions for the modified KdV and the generalized KdV equations via Exp-function method, J. Math. Ext., 4 (2010), 77–98.
  • [27] J. Manafian Heris and M. Fazli Aghdaei, Application of the Exp-function method for solving the combined KdV-mKdV and Gardner-KP equations, Math. Sci., 6 (2012), 68.
  • [28] J. Manafianheris, Solving the integro-differential equations using the modified Laplace Adomian decomposition method, J. Math. Ext., 6 (2012), 41–55.
  • [29] 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. Numer. Anal., 2013 (2013), 1–18.
  • [30] J. Manafian Heris and I. Zamanpour, Analytical treatment of the coupled Higgs equation and the Maccari system via Exp-Function Method, Acta Univ. Apulensis, 33 (2013), 203–216.
  • [31] J. Manafian and I. Zamanpour, Exact travelling wave solutions of the symmetric regularized long wave (SRLW) using analytical methods, Stat. Optim. Inf. Comput., 2 (2014), 47–55.
  • [32] J. Manafian and M. Lakestani, Optical solitons with Biswas-Milovic equation for Kerr law nonlinearity, Eur. Phys. J. Plus, 130 (2015), 61.
  • [33] J. Manafian and M. Lakestani, Solitary wave and periodic wave solutions for Burgers, Fisher, Huxley and combined forms of these equations by the (G’/G)-expansion method, Pramana, 130 (2015), 31–52.
  • [34] J. Manafian, O. A. Ilhan, L. Avazpour, and A. Alizadeh, Localized waves and interaction solutions to the fractional generalized CBS-BK equation arising in fluid mechanics, Adv. Differ. Equ., 141 (2021), 2021.
  • [35] X. H. Menga, W. J. Liua, H. W. Zhua, C. Y. Zhang, and B. Tian, Multi-soliton solutions and a Bäcklund transformation for a generalized variable-coefficient higher-order nonlinear Schrödinger equation with symbolic computation, Phys. A, 387 (2008), 97–107.
  • [36] A. K. Mutashar, A. Hatem, and M. A. Hussein, A New Analytical and Numerical Solutions for Biological Population Models by Kamal Adomian Decomposition Method, Adv. Math. Models Appl., (2025).
  • [37] J. K. Perring and T. H. Skyrme, A model unified field equation, Nucl. Phys., 31 (1962), 550–555.
  • [38] Y. Qian, J. Manafian, M. Asiri, K. H. Mahmoud, A. I. Alanssari, and A. S. Alsubaie, Nonparaxial solitons and the dynamics of solitary waves for the coupled nonlinear Helmholtz systems, Opt. Quantum Electron., 55 (2023), 1022.
  • [39] A. R. Seadawy and J. Manafian, New soliton solution to the longitudinal wave equation in a magneto-electro- elastic circular rod, Results Phys., 8 (2018), 1158–1167.
  • [40] C. A. G. Sierra and A. H. Salas, The generalized tanh-coth method to special types of the fifth-order KdV equation, Appl. Math. Comput., 203 (2008), 873–880.
  • [41] Sirendaoreji and S. Jiong, A direct method for solving sinh-Gordon type equation, Phys. Lett. A, 298 (2002), 133–139.
  • [42] L. Sun, J. Manafian, O. A. Ilhan, M. Abotaleb, A. Y. Oudah, and A. S. Prakaash, Theoretical analysis for miscellaneous soliton waves in metamaterials model by modification of analytical solutions, Opt. Quantum Electron., 54 (2022), 651.
  • [43] K. U. Tariq, J. Manafian, S. Malmir, R. N. Tufail, and O. A. Ilhan, On the structure of the higher dimensional Date-Jimbo-Kashiwara-Miwa model emerging in water waves, Discov. Appl. Sci., (2025).
  • [44] W. Wang, K. Hasanirokh, J. Manafian, M. Abotaleb, and Y. Yang, Analytical approach for polar magnetooptics in multilayer spin-polarized light emitting diodes based on InAs quantum dots, Opt. Quantum Electron., 54 (2022), 137.
  • [45] A. M. Wazwaz, The tanh method for travelling wave solutions of nonlinear equations, Appl. Math. Comput.,154 (2004), 713–723.
  • [46] A. M. Wazwaz, The tanh method: exact solutions of the sine-Gordon and the Sinh-Gordon equations, Appl. Math. Comput., 167 (2005), 1196–1210.
  • [47] A. M. Wazwaz, Travelling wave solutions for combined and double combined sine-cosine-Gordon equations by the variable separated ODE method, Appl. Math. Comput., 177 (2006), 755–760.
  • [48] A. M. Wazwaz, The variable separated ODE and the tanh methods for solving the combined and the double combined sinh-cosh-Gordon equations, Appl. Math. Comput., 177 (2006), 745–754.
  • [49] G. W. Wei, Discrete singular convolution for the sinh-Gordon equation, Physica D, 137 (2000), 247–259.
  • [50] G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, New York, NY, 1999.
آمار
تعداد مشاهده مقاله: 580
تعداد دریافت فایل اصل مقاله: 429


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب