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Dergiler / Turkish Journal of Mathematics and Computer Science / 2013 / Volume: 1

Solutions of Nonlinear Partial Differential Equations Using Generalized Hyperbolic Functions

Yusuf Pandir(Department of Mathematics, Faculty of Science and Art, Bozok University, 66100 Yozgat, Turkey)
Halime Ulusoy(Department of Mathematics, Faculty of Science and Art, Bozok University, 66100 Yozgat, Turkey)
Sayfa
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Yayın Tarihi
2016-05-26
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Also, physical reviews of the solutions are added.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:In this article, with the help of generalized hyperbolic functions a new version of the classic sech-function method is defined.
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Temel Bulgular & Veri:The developed method is applied to the nonlinear partial differential equations and a general form of solution function called as ” 1-soliton ” is obtained.
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Sonuç & Katkı:Also, physical reviews of the solutions are added.
🔬Tür:Literatür & Derleme Çalışması
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Generalized hyperbolic functions · generalized regularized long wave equation · (2+1) dimensional Boussinesq equation

Abstract

In this article, with the help of generalized hyperbolic functions a new version of the classic sech-function method is defined. The developed method is applied to the nonlinear partial differential equations and a general form of solution function called as ” 1-soliton ” is obtained. New exact solutions of generalized regularized long wave equation (GRLW) and the (2+1) dimensional Boussinesq equation found. Also, physical reviews of the solutions are added.

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Bu Makaleye Atıf Yap

Pandir, Y., Ulusoy, H. (2016). Solutions of Nonlinear Partial Differential Equations Using Generalized Hyperbolic Functions. Turkish Journal of Mathematics and Computer Science, Volume: 1. https://ajindex.com/articles/1324991

Kaynakça (22)

  1. Kudryashov N. A., One method for finding exact solutions of nonlinear differential equations, Commun. Nonl. Sci. Numer. Simulat., 17, 2248-2253 (2012).
  2. Pandir Y., Gurefe Y., Misirli E., A new approach to KudryashovÆs method for solving some nonlinear physical models, Int. J. Phys. Sci., 7(21), 2860-2866 (2012).
  3. Pandir Y., Tandogan Y.A., Solutions of the nonlinear differential equations by use of symmetric functions, Int. J. Appl. Math., 26(3), 403-410 (2013).
  4. Malfliet W., Hereman W., Misirli E., The tanh method: exact solutions of nonlinear evolution and wave equations, Phys. Scr., 54, 563-568 (1996).
  5. Misirli E., Gurefe Y., Exp-function method for solving nonlinear evolution equations, Math. Comput. Appl., 16, 258-266 (2011).
  6. Gurefe Y., Misirli E., Exp-function method for solving nonlinear evolution equations with higher order nonlinearity, Comput. Math. Appl., 61, 2025-2030 (2011).
  7. Gurefe Y., Pandir Y., and Misirli E., New exact solutions of stochastic KdV equation, Appl. Math. Sci., 6(65), 3225-3234 (2012).
  8. Wang M., Li X., Zhang J., The (G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A, 372, 417-423 (2008).
  9. Liu C.S., Trial equation method and its applications to nonlinear evolution equations, Acta. Phys. Sin., 54, 2505-2509 (2005).
  10. Liu C.S., A new trial equation method and its applications, Commun. Theor. Phys., 45, 395-397 (2006).
  11. Jun C.Y., Classification of traveling wave solutions to the Vakhnenko equations, Comput. Math. Appl., 62, 3987-3996 (2011).
  12. Jun C.Y., Classification of traveling wave solutions to the modified form of the Degasperis-Procesi equation, Math. Comput. Model., 56, 43-48 (2012).
  13. Pandir Y., Gurefe Y., Kadak U., Misirli E., Classifications of exact solutions for some nonlinear partial differential equations with generalized evolution, Abstr. Appl. Anal., 2012, Article ID 478531 16 pages (2012).
  14. Ren Y., Zhang H., New generalized hyperbolic functions and auto-Bocklund transformation to find new exact solutions of the (2+1)-dimensional NNV equation, Phys. Lett. A, 357, 438-448 (2006).
  15. Ismail, M.S., Biswas, A., 1-Soliton solution of the generalized KdV equation with generalized evolution, Appl. Math. Comput., 216, 1673-1679 (2010).
  16. Yomba, E., Generalized hyperbolic functions to find soliton-like solutions for a system of coupled nonlinear Schrodinger equations, Phys. Lett. A, 372, 1612-1618 (2008).
  17. Stakhov, A., Rozin, B., On a new class of hyperbolic functions, Chaos Soliton. Fract., 23, 379-389 (2005).
  18. Pandir Y., Ulusoy H., New generalized hyperbolic functions to find new exact solutions of the nonlinear partial differential equations, J. Math., 2013, Article ID 201276, 5 pages (2013).
  19. Ren Y.J., Korteweg-de Vries Equation (KdV), Different Analytical Methods for Solving the, Mathematics of complexity and dynamical systems, New York, Springer, (2012).
  20. El-Boree M.K., Hyperbolic and trigonometric solutions for some nonlinear evolution equations, Commun.Nonlinear Sci., 17(11), 4085-4096 (2012).
  21. Raslan K. R., Hassan S.M., Solitary waves for the MRLW equation, Appl. Math. Let., 22, 984-989 (2009).
  22. A.S.A. Rady, E.S. Osman, M. Khalfallah, On soliton solutions of the (2 + 1) dimensional Boussinesq equation, Appl. Math. Comput., 219, 3414-3419 (2012).