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

 آمار

تعداد نشریات43
تعداد شماره‌ها1,224
تعداد مقالات15,038
تعداد مشاهده مقاله50,578,606
تعداد دریافت فایل اصل مقاله13,668,690
Akbulut, Arzu, Islam, Rayhanul, Arafat, Yiasir, Taşcan, Filiz. (1402). A novel scheme for SMCH equation with two different approaches. سامانه مدیریت نشریات علمی, 11(2), 263-280. doi: 10.22034/cmde.2022.50363.2093
Arzu Akbulut; Rayhanul Islam; Yiasir Arafat; Filiz Taşcan. "A novel scheme for SMCH equation with two different approaches". سامانه مدیریت نشریات علمی, 11, 2, 1402, 263-280. doi: 10.22034/cmde.2022.50363.2093
Akbulut, Arzu, Islam, Rayhanul, Arafat, Yiasir, Taşcan, Filiz. (1402). 'A novel scheme for SMCH equation with two different approaches', سامانه مدیریت نشریات علمی, 11(2), pp. 263-280. doi: 10.22034/cmde.2022.50363.2093
Akbulut, Arzu, Islam, Rayhanul, Arafat, Yiasir, Taşcan, Filiz. A novel scheme for SMCH equation with two different approaches. سامانه مدیریت نشریات علمی, 1402; 11(2): 263-280. doi: 10.22034/cmde.2022.50363.2093

A novel scheme for SMCH equation with two different approaches

Computational Methods for Differential Equations
مقاله 5، دوره 11، شماره 2، تیر 2023، صفحه 263-280    اصل مقاله (888.04 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2022.50363.2093
نویسندگان
Arzu Akbulut* 1؛ Rayhanul Islam2؛ Yiasir Arafat2؛ Filiz Taşcan3
1Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Bursa, Turkey.
2Department of Mathematics, Pabna University of Science and Technology, Pabna-Bangladesh.
3Faculty of Arts and Science, Department of Mathematics and Computer, Eski¸sehir Osmangazi University, Eskisehir, Turkey.
چکیده
In this study, the unified and improved F-expansion methods are applied to derive exact traveling wave solutions of the simplified modified Camassa-Holm (SMCH) equation. The current methods can calculate all branches of solutions at the same time, even if several solutions are quite near and therefore impossible to identify via numerical methods. All obtained solutions are given by hyperbolic, trigonometric, and rational function solutions which obtained solutions are useful for real-life problems in fluid dynamics, optical fibers, plasma physics and so on. The two-dimensional (2D) and three-dimensional (3D) graphs of the obtained solutions are plotted. Finally, we can state that these strategies are extremely successful, dependable, and simple. These ideas might potentially be applied to many nonlinear evolution models in mathematics and physics. 
کلیدواژه‌ها
SMCH equation؛ The improved F-expansion method؛ The unified method؛ Symbolic computation؛ Exact solution؛ Solitary wave
مراجع
  • [1] M. A. Akbar and M. A. Norhashidah, The improved F-expansion method with Riccati equation and its applications in mathematical physics, Cogent Math., 4 (2017), 1-19.
  • [2] S. Ak¸ca˘gıl and T. Aydemir, A new application of the unified method, New Trend Math. Sci., 6(1) (2018), 185-199.
  • [3] A. Ali, M. A. Iqbal, and S. T. Mohyud-Din, Traveling wave solutions of generalized Za- kharov–Kuznetsov–Benjamin–Bona–Mahony and simplified modified form of Camassa–Hol equation exp(–ψ(η))– Expansion method, Egypt. J. Basic Appl. Sci., 3 (2016), 134–140.
  • [4] S. M. Y. Arafat, S. M. R. Islam, and M. H. Bashar, Influence of the free parameters and obtained wave solutions from CBS equation, Int. J. Appl. Math., 8 (2022), 1-17.
  • [5] M. H. Bashar and S. M. R. Islam, Exact solutions to the (2+1)-Dimensional Heisenberg ferromagnetic spin chain equation by using modified simple equation and improve F-expansion methods, Phys. Open 5 (2020), 1-9.
  • [6] M. H. Bashar, S. M. R. Islam, and D. Kumar, Construction of traveling wave solutions of the (2+1)-Dimensional Heisenberg ferromagnetic spin chain equation, Partial. Differ. Equ. App. Math., 4 (2021), 1-9.
  • [7] M. H. Bashar, S. M. Y. Arafat, S. M. R. Islam, and M. M. Rahman, Wave solutions of the couple Drin- fel’d–Sokolov–Wilson equation: new wave solutions and free parameters effect, J. Ocean Eng. Sci., In Press (2022). https://doi.org/10.1016/j.joes.2022.05.003
  • [8] M. Bilal, J. Ren, and U. Younas, Stability analysis and optical soliton solutions to the nonlinear Schr¨odinger model with efficient computational techniques, Opt. Quantum Electron, 53 (2021), 1-19.
  • [9] M. Bilal, U. Younas, and J. Ren, Propagation of diverse solitary wave structures to the dynamical soliton model in mathematical physics, Opt. Quantum Electron, 53 (2021), 1-20.
  • [10] M. Bilal, U. Younas, and J. Ren Dynamics of exact soliton solutions in the double chain model of deoxyribonucleic acid, Math. Methods Appl. Sci., 44 (2021), 13357-13375.
  • [11] M. Bilal, U. Younas, and J. Ren, Dynamics of exact soliton solutions to the coupled nonlinear system using reliable analytical mathematical approaches, Commun. Theor. Phys., 73 (2021), 085005.
  • [12] J. P. Boyd, Peakons and cashoidal waves: traveling wave solutions of the Camassa–Holm equation, Appl. Math. Comput., 81(2–3) (1997), 173–187.
  • [13] R. Camassa and D. Holm, An integrable shallow water equation with peaked soliton, Phys. Rev. Lett., 71 (1993), 1661–1664.
  • [14] S. J. Chen, X. Lu, and W. X. Ma, Backlund transformation, exact solutions and interaction behaviour of the (3+1)- dimensional Hirota–Satsuma-Ito-like equation, Commun. Nonlinear Sci. Numer. Simul., 83 (2020), 1-12.
  • [15] F. Cooper and H. Shepard, Solitons in the Camassa–Holm shallow water equation, Phys. Lett. A, 194 (1994) 246–250.
  • [16] M. Fisher and J. Shiff, The Camassa–Holm equation: conserved quantities and the initial value problem, Phys. Lett. A, 259(3) (1999), 371–376.
  • [17] Y. Gao, L. Li, and J. G. Liu, Patched peakon weak solutions of the modified Camassa–Holm equation, Phys. D: Nonlinear Phenom., 390 (2019), 15-35. https://doi.org/10.1016/j.physd.2018.10.005
  • [18] O. M. G¨ozu¨kızıl, S. Ak¸ca˘gıl, and T. Aydemir, Unification of all hyperbolic tangent function methods, Open Phys., 14 (2016), 524–541.
  • [19] S. M. R. Islam, The traveling wave solutions of the cubic nonlinear Schr¨odinger equation using the enhanced (G//G)-expansion method, World Appl. Sci. J., 33(4) (2015), 659-667.
  • [20] S. M. R. Islam, Application of an enhanced (G//G)-expansion method to find exact solutions of nonlinear PDEs in particle physics, Am. J. Appl. Sci., 12(11) (2015), 836-846.
  • [21] S. M. R. Islam, A. Akbulut, and S. M. Y. Arafat, Exact solutions of the different dimensional CBS equations in mathematical physics, Partial Differ. Equ. App. Math., 5 (2022), 1-7.
  • [22] S. Islam, K. Khan, and M. A. Akbar, Application of the improved F -expansion method with Riccati equation to find the exact solution of the nonlinear evolution equations, J. Egypt. Math. Soc., 25 (2017), 13–18.
  • [23] M. N. Islam, M. Asaduzzaman, and M. S. Ali, Exact wave solutions to the simplified modified Camassa-Holm equation in mathematical physics, AIMS Math., 5(1) (2019), 26-41.
  • [24] S. M. R. Islam, S. M. Y. Arafat, and H. F. Wang, Abundant closed-form wave solutions to the simplified modified Camassa-Holm equation, J. Ocean Eng. Sci., In Press (2022). https://doi.org/10.1016/j.joes.2022.01.012
  • [25] S. M. R. Islam, K. Khan, and K. M. A. Al-Woadud, Analytical studies on the Benney-Luke equation in mathe- matical physics, Wave Random Complex, 28 (2018), 300-309.
  • [26] S. M. R. Islam, K. Khan, and M. A. Akbar, Exact solution of unsteady Korteweg-de Vries and time regularized long wave equations, Springerplus, 4 (2015), 1-11.
  • [27] M. Kaplan and A. Akbulut, The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method, Opt. Quantum Electron, 53 (2021), 1-21.
  • [28] D. Kumar, C. Park, N. Tamanna, G. C. Paul, and M. S. Osman, Dynamics of two-mode Sawada-Kotera equation: Mathematical and graphical analysis of its dual-wave solutions, Results Phys., 19 (2020), 1-11.
  • [29] Y. Li, L. Tian, and Y. Wu, On the Bifurcation of traveling wave solution of generalized Camassa-Holm equation, Int. J. Nonlinear Sci., 6(1) (2008), 34-45.
  • [30] X. Liu, L. Tian, and Y. Wu, Application of (G//G)-expansion method to two nonlinear evolution equations, App. Math. Comput., 217 (2010), 1376-1384.
  • [31] X. Lu, L. Lu, and A. Chen, New peakons and periodic peakons of the modified Camassa-Holm equation, J. Nonlinear Model. Analy., 2(3) (2020), 345-353.
  • [32] M. H. Raddadi, M. Younis, A. R. Seadawy, S. U. Rehman, M. Bilal, S. T. R. Rizvi, and A. Althobaiti, Dynamical behaviour of shallow water waves and solitary wave solutions of the Dullin-Gottwald-Holm dynamical system, J. King Saud Univ. Sci., 33 (2021), 1-9. https://doi.org/10.1016/j.jksus.2021.101627
  • [33] S. U. Rehman, A. R. Seadawy, S. T. R. Rizvi, S. Ahmed, and S. Althobaiti, Investigation of double dispersive waves in nonlinear elastic inhomogeneous Murnaghan’s rod, Mod. Phys. Lett. B, 36 (2022), 1-12.
  • [34] S. U. Rehman and J. Ahmad, Dispersive multiple lump solutions and soliton’s interaction to the nonlinear dy- namical model and its stability analysis, Eur. J. Plus 76 (2022), 1-13.
  • [35] S. U. Rehman, M. Bilal, and J. Ahmad, Dynamics of soliton solutions in saturated ferromagnetic materials by a novel mathematical method, J. Magn. Magn. Mater., 538 (2021), 1-12.
  • [36] A. R. Seadawy, A. Ali, S. Althobaiti, and A. Sayed, Propagation of wave solutions of nonlinear Heisenberg ferromagnetic spin chain and Vakhnenko dynamical equations arising in nonlinear water wave models, Chaos Solitons Fractals, 146(2021), 1-11.
  • [37] A. R. Seadawy, S. U. Rehman, M. Younis, S. T. R. Rizvi, and S. Althobaiti, On solitons: Propagation of shallow water waves for the fifth-order KdV hierarchy integrable equation, Open Phys., 19 (2021), 828-842.
  • [38] A. R. Seadawy, S. U. Rehman, M. Younis, S. T. R. Rizvi, S. Althobaiti, and M. M. Makhlouf, Modulation instability analysis and longitudinal wave propagation in an elastic cylindrical rod modelled with Pochhammer- Chree equation, Phys. Scr., 96 (2021), 1-14.
  • [39] Y. Shen, B. Tian, C. R. Zhang, H. Y. Tian, and S. H. Liu, Breather-wave, periodic-wave and traveling wave solutions for a (2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation for an incompressible fluid, Mod. Phys. Lett. B, 35 (2021), 1-10.
  • [40] S. F. Tian, Lie symmetry analysis, conservation laws and solitary wave solutions to a fourth-order nonlinear generalized Boussinesq water wave equation, App. Math. Lett., 100 (2020), 1-8.
  • [41] L. Tian and X. Song, New peaked solitary wave solutions of the generalized Camassa–Holm equation, Chaos Solitons Fractals, 19 (2004), 621–637.
  • [42] L. Tian, G. Xu, and Z. Liu, The concave or convex peaked and smooth solutions of Camassa–Holm equation, Appl. Math. Mech., 23(5) (2002), 557–567.
  • [43] G. Wang, A new (3 + 1)-dimensional Schr¨odinger equation: derivation, soliton solutions and conservation laws, Nonlinear Dyn., 104 (2021) 1595–1602.
  • [44] G. Wang, Q. P. Liu, and H. Mao, The modified Camassa- Holm equation: B¨acklund transformation and nonlinear superposition formula, J. Phys. A Math. Theor., 53 (2020), 1-15.
  • [45] A. M. Wazwaz, New compact and noncompact solutions for two variants of a modified Camassa-Holm equation, Appl. Math. Comput., 163(3) (2005), 1165-1179.
  • [46] A. Yoku¸s, H. Durur, and K. A. Abro, Symbolic computation of Caudrey–Dodd–Gibbon equation subject to periodic trigonometric and hyperbolic symmetries, Eur. Phys. J. Plus, 136 (2021), 1-16.
  • [47] U. Younas and J. Ren, Investigation of exact soliton solutions in magneto-optic waveguides and its stability analysis, Results Phys.,21 (2021), 1-20.
  • [48] U. Younas, H. Rezazadeh, J. Ren, and M. Bilal, Propagation of diverse exact solitary wave solutions in separation phase of iron (Fe-Cr- X (X=Mo, Cu)) for the ternary alloys, Int. J. Mod. Phys. B 36 (2022), 1-18.
  • [49] U. Younas, J. Ren, and M. Bilal, Dynamics of optical pulses in fiber optics, Mod. Phys. Lett. B, 36 (2022), 1-27.
  • [50] U. Younas, M. Bilal, and J. Ren, Propagation of the pure-cubic optical solitons and stability analysis in the absence of chromatic dispersion, Opt. Quantum Electron., 53 (2021), 1-25.
  • [51] U. Younas, M. Bilal, and J. Ren, Diversity of exact solutions and solitary waves with the influence of damping effect in ferrites materials, J. Magn. Magn. Mater., 549 (2022), 1-12.
  • [52] W. Yu, W. Liu, H. Triki, Q. Zhou, and A. Biswas, Phase shift, oscillation and collision of the anti-dark solitons for the (3+1)-dimensional coupled nonlinear Schr¨odinger equation in an optical fiber communication system, Nonlinear Dyn., 97 (2019), 1253–1262.
  • [53] D. Zhao and Zhaqilao, Three-wave interactions in a more general (2+1)-dimensional Boussinesq equation, Eur. Phys. J. Plus, 135 (2020), 1-16.
آمار
تعداد مشاهده مقاله: 407
تعداد دریافت فایل اصل مقاله: 404


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب