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

 آمار

تعداد نشریات44
تعداد شماره‌ها1,353
تعداد مقالات16,546
تعداد مشاهده مقاله53,674,912
تعداد دریافت فایل اصل مقاله16,149,217
Aydın, Zeynep, Taşcan, Filiz. (1403). Application of new Kudryashov method to Sawada-Kotera and Kaup-Kupershmidt equations. سامانه مدیریت نشریات علمی, 13(2), 608-617. doi: 10.22034/cmde.2024.60001.2558
Zeynep Aydın; Filiz Taşcan. "Application of new Kudryashov method to Sawada-Kotera and Kaup-Kupershmidt equations". سامانه مدیریت نشریات علمی, 13, 2, 1403, 608-617. doi: 10.22034/cmde.2024.60001.2558
Aydın, Zeynep, Taşcan, Filiz. (1403). 'Application of new Kudryashov method to Sawada-Kotera and Kaup-Kupershmidt equations', سامانه مدیریت نشریات علمی, 13(2), pp. 608-617. doi: 10.22034/cmde.2024.60001.2558
Aydın, Zeynep, Taşcan, Filiz. Application of new Kudryashov method to Sawada-Kotera and Kaup-Kupershmidt equations. سامانه مدیریت نشریات علمی, 1403; 13(2): 608-617. doi: 10.22034/cmde.2024.60001.2558

Application of new Kudryashov method to Sawada-Kotera and Kaup-Kupershmidt equations

Computational Methods for Differential Equations
مقاله 18، دوره 13، شماره 2، خرداد 2025، صفحه 608-617    اصل مقاله (1019.37 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2024.60001.2558
نویسندگان
Zeynep Aydın* ؛ Filiz Taşcan
Faculty of Science, Department of Mathematics and Computer, Eskisehir Osmangazi University, Eskisehir, Turkey.
چکیده
In this article, with the help of the new Kudryashov method, we examine general solutions to the (2+1)-dimensional Sawada-Kotera equation (SKE) and Kaup-Kupershmidt (KK) equation. Using Maple, a symbolic computing application, it was shown that all obtained solutions are given by hyperbolic, exponential and logaritmic function solutions which obtained solutions are useful for fluid dynamics, optics and so on. Finally, we have presented some graphs for general solutions of these equations with special parameter values. The reliability and scope of programming provide eclectic applicability to high-dimensional nonlinear evolution equations for the development of this method. The results found gave us important information regarding the applicability of the new Kudryashov method.
کلیدواژه‌ها
Exact solutions؛ Travelling wave solutions؛ Nonlinear partial differential equations
مراجع
  • [1] A. H. Bhrawy, et al., Dispersive optical solitons with SchrodingerHirota equation., Journal of Nonlinear Optical Physics & Materials, 23(01) (2014), 1450014.
  • [2] G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York, 1989.
  • [3] Y. Chen, et al., Dark wave, rogue wave and perturbation solutions of Ivancevic option pricing model., Nonlinear Dynamics, 105 (2021), 2539–2548.
  • [4] K. Debin , H. Rezazadeh , N. Ullah , J. Vahidi, U. T. Kalim, and L. Akinyemi, New soliton wave solutions of a (2+1)-dimensional Sawada-Kotera equation, Journal of Ocean Engineering and Science, 8 (2023), 527–532.
  • [5] M. Eslami, M. Mirzazadeh, and A. Biswas, Soliton solutions of the resonant nonlinear Schrodinger's equation in optical fibers with time dependent coefficients by simplest equation approach, J. Mod. Opt., 60(19) (2013), 16271636.
  • [6] M. R. A. Fahim, et al., Wave profile analysis of a couple of (3+ 1)-dimensional nonlinear evolution equations by sine-Gordon expansion approach. Journal of Ocean Engineering and Science, 7(3) (2022), 272279.
  • [7] E. Fan and H. Zhang, A note on the homogeneous balance method, Phys. Lett., A 246 (1998), 403406.
  • [8] Z. S. Feng, The First integral method to study the Burgers-KdV equation, J. Phys. A: Math. Gen., 35 (2002), 343349.
  • [9] A. K. Gupta and S. S. Ray., Numerical treatment for the solution of fractional fifth-order SawadaKotera equation using second kind Chebyshev wavelet method Applied Mathematical Modelling, 39 (2015), 51215130.
  • [10] J. H. He and X. H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons & Fractals, 30(3) (2006), 700708.
  • [11] J. H. He, Approximate solution of nonlinear differential equations with convolution product nonlinearities, Computer Methods in Applied Mechanics and Engineering, 167(1-2) (1998), 6973.
  • [12] R. Hirota, The Direct Method in Soliton Theory, Cambridge University Pres, Cambridge, 2004.
  • [13] D. Kaup, On the inverse scattering problem for the cubic eigenvalue problems of the class ψ3x + 6Qψx + 6Rψ = λψ, Stud. Appl. Math., 62 (1980), 189216.
  • [14] A. Khaled, The Modified Kudryashov Method for Solving Some Seventh Order Nonlinear PDEs, Mathematical Physics, 11 (2015), 308319.
  • [15] A. Kilicman and R. Silambarasan, Modified Kudryashov method to solve generalized Kuramoto-Sivashinsky equation, Symmetry 10, 10 (2018), 527.
  • [16] N. A. Kudryashov, One method for finding exact solutions of nonlinear differential equations, Commun. Nonlinear Sci. Numer. Simul. Commun. Nonlinear Sci. Number, 17 (2011).
  • [17] N. A. Kudryashov, Method of the logistic function for finding analytical solutions of nonlinear differential equations, Model. Anal. Inf. Syst., 22 (2015), 2337.
  • [18] N. A. Kudryashov, Logistic function as solution of many nonlinear differential equations, Appl. Math. Model., 39(18) (2015), 57335742.
  • [19] N. A. Kudryashov, Method for finding highly dispersive optical solitons of nonlinear differential equations, Optik, 206 (2020), 63550.
  • [20] B. A. Kupershmidt, A super KdV equation: an integrable system, Phys. Lett. A, 102 (1984), 213215.
  • [21] W. X. Ma, R. Zhou, and L. Gao, Exact one-periodic and two-periodic wave solutions to Hirota bilinear equations in (2+1) dimensions., Modern Physics Letters A, 24(21) (2009), 16771688.
  • [22] C. L. Mader, Numerical Modeling of Water Waves, Numerical Modeling of Water Waves, Jun. 2004.
  • [23] W. Malfliet and W. Hereman, The tanh method. I: exact solutions of nonlinear evolution and wave equations, Phys. Scripta, 54 (1996), 563568.
  • [24] R. M. Miura, Backlund Transformation, Springer-Verlag, New York, 1973.
  • [25] M. Ozisik, A. Secer, M. Bayram, and H. Aydin, An encyclopedia of Kudryashov's integrability approaches applicable to optoelectronic devices, Optik, 265 (2022), 169499.
  • [26] K. Sawda and T. Kotera, A Method Finding N-Soliton Solutions of the Kdv and KdV-Like Equations, Prog. Theor. Phys., 51 (1974), 135567.
  • [27] H. Srivastava, D. Baleanu, M. T. M. Jos, H. Rezazadeh, S. Arshed, and G. Hatira, Traveling wave solutions to nonlinear directional couplers by modified Kudryashov method, Phys. Scr., 95 (2020), 075217.
  • [28] M. Wang, X. Li, and J. Zhang, The (G/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A., 372 (2008), 417423.
  • [29] M. L. Wang, Solitary wave solutions for variant Boussinesq equations, Phys. Lett. A, 199 (1995), 169172.
  • [30] A. M. Wazwaz, The tanhcoth method for solitons and kink solutions for nonlinear parabolic equations, Appl. Math. Comput. 188 (2007), 14671475.
  • [31] A. M. Wazwaz, Abundant solitons solutions for several forms of the fifth-order KdV equation by using the tanh method, Appl. Math.Comput., 182 (2006), 283300.
  • [32] C. Yan, A simple transformation for nonlinear waves, Phys. Lett. A., 224 (1996), 7784.
  • [33] C. Yan, A simple transformation for nonlinear waves, Physics Letters A, 224(1-2) (1996), 7784.
  • [34] A. Yildirim, A. S. Paghaleh, M. Mirzazadeh, and H. Moosaei, A. Biswas, New exact traveling wave solutions for DS-I and DS- II equations, Nonlinear Anal.: Modell. Control. 17(3) (2012), 369378.
  • [35] E. M. E. Zayed, R. M. A. Shohib, and M. E. M. Alngar, Cubic-quartic optical solitons in Bragg gratings fibers for NLSE having parabolic non-local law nonlinearity using two integration schemes, Optical and Quantum Electronics, 53(8) (2021), 452.
  • [36] E. M. E. Zayed, M. E. M. Alngar, and R. M. A. Shohib, Cubic-quartic embedded solitons with χ (2) and χ (3) nonlinear susceptibilities having multiplicative white noise via It calculus, Chaos, Solitons & Fractals, 168 (2023), 113186.
  • [37] E. M. E. Zayed, et al. Solitons in magneto-optics waveguides for the nonlinear BiswasMilovic equation with Kudryashov's law of refractive index using the unified auxiliary equation method. Optik, 235 (2021), 166602.
 

آمار
تعداد مشاهده مقاله: 233
تعداد دریافت فایل اصل مقاله: 266


سامانه مدیریت نشریات علمی. قدرت گرفته از سیناوب