CFP last date
20 January 2025
Reseach Article

Exact Traveling Wave Solution for Nonlinear Fractional Partial Differential Equation Arising in Soliton using the exp(-f(h))-Expansion Method

by Emad H. M. Zahran
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 109 - Number 13
Year of Publication: 2015
Authors: Emad H. M. Zahran
10.5120/19247-0619

Emad H. M. Zahran . Exact Traveling Wave Solution for Nonlinear Fractional Partial Differential Equation Arising in Soliton using the exp(-f(h))-Expansion Method. International Journal of Computer Applications. 109, 13 ( January 2015), 12-17. DOI=10.5120/19247-0619

@article{ 10.5120/19247-0619,
author = { Emad H. M. Zahran },
title = { Exact Traveling Wave Solution for Nonlinear Fractional Partial Differential Equation Arising in Soliton using the exp(-f(h))-Expansion Method },
journal = { International Journal of Computer Applications },
issue_date = { January 2015 },
volume = { 109 },
number = { 13 },
month = { January },
year = { 2015 },
issn = { 0975-8887 },
pages = { 12-17 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume109/number13/19247-0619/ },
doi = { 10.5120/19247-0619 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:44:41.534006+05:30
%A Emad H. M. Zahran
%T Exact Traveling Wave Solution for Nonlinear Fractional Partial Differential Equation Arising in Soliton using the exp(-f(h))-Expansion Method
%J International Journal of Computer Applications
%@ 0975-8887
%V 109
%N 13
%P 12-17
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The exp((-?(?))-expansion method is used as the first time to investigate the wave solution of a nonlinear the space-time nonlinear fractional PKP equation, the space-time nonlinear fractional SRLW equation, the space-time nonlinear fractional STO equation and the space-time nonlinear fractional KPP equation. The proposed method also can be used for many other nonlinear evolution equations.

References
  1. M. J. Ablowitz, H. Segur, Solitions and Inverse Scattering Transform, SIAM, Philadelphia 1981.
  2. W. Malfliet, Solitary wave solutions of nonlinear wave equation, Am. J. Phys. , 60 (1992) 650-654.
  3. W. Malfliet, W. Hereman, The tanh method: Exact solutions of nonlinear evolution and wave equations, Phys. Scr. , 54 (1996) 563-568.
  4. A. M. Wazwaz, The tanh method for travelling wave solutions of nonlinear equations, Appl. Math. Comput. , 154 (2004) 714-723.
  5. S. A. EL-Wakil, M. A. Abdou, New exact travelling wave solutions using modified extented tanh-function method, Chaos Solitons Fractals, 31 (2007) 840-852.
  6. E. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277 (2000) 212-218.
  7. A. M. Wazwaz, The extended tanh method for abundant solitary wave solutions of nonlinear wave equations, Appl. Math. Comput. , 187 (2007) 1131-1142.
  8. A. M. Wazwaz, Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE. method, Comput. Math. Appl. , 50 (2005) 1685-1696.
  9. A. M. Wazwaz, A sine-cosine method for handling nonlinear wave equations, Math. Comput. Modelling, 40 (2004) 499-508.
  10. C. Yan, A simple transformation for nonlinear waves, Phys. Lett. A 224 (1996) 77-84.
  11. Emad. H. M. Zahran and mostafa M. A. Khater. The modified simple equation method and its applications for solving some nonlinear evolutions equations in mathematical physics. Jokull journal- Vol. 64. Issue 5 - May 2014.
  12. M. A. Abdou, The extended F-expansion method and its application for a class of nonlinear evolution equations, Chaos Solitons Fractals, 31 (2007) 95-104.
  13. Y. J. Ren, H. Q. Zhang, A generalized F-expansion method to find abundant families of Ja-cobi elliptic function solutions of the (2+l)-dimensional Nizhnik-Novikov-Veselov equation, Chaos Solitons Fractals, 27 (2006) 959-979.
  14. J. L. Zhang, M. L. Wang, Y. M. Wang, Z. D. Fang, The improved F-expansion method and its applications, Phys. Lett. A 350 (2006) 103-109.
  15. J. H. He, X. H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fractals 30 (2006) 700-708.
  16. H. Aininikhad, H. Moosaei, M. Hajipour, Exact solutions for nonlinear partial differential equations via Exp-function method, Numer. Methods Partial Differ. Equations, 26 (2009) 1427-1433.
  17. Z. Y. Zhang, New exact traveling wave solutions for the nonlinear Klein-Gordon equation, Turk. J. Phys. , 32 (2008) 235-240.
  18. M. L. Wang, J. L. Zhang, X. Z. Li, The (G^,/G)- expansion method and travelling wave solutions of nonlinear evolutions equations in mathematical physics, Phys. Lett. A 372 (2008) 417-423.
  19. Emad H. M. Zahran and Mostafa M. A. Khater, Exact solutions to some nonlinear evolution equations by using (G'/G)-expansion method, Jokull journal- Vol. 64. Issue 5 - May 2014.
  20. E. M. E. Zayed and K. A. Gepreel, The (G^,/G)- expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics, J. Math. Phys. , 50 (2009) 013502-013513.
  21. E. M. E. Zayed, The (G^,/G)- expansion method and its applications to some nonlinear evolu¬tion equations in mathematical physics, J. Appl. Math. Computing, 30 (2009) 89-103.
  22. C. Q. Dai , J. F. Zhang, Jacobian elliptic function method for nonlinear differential difference equations, Chaos Solutions Fractals, 27 (2006) 1042-1049.
  23. Emad H. M. Zahran and Mostafa M. A. Khater, Exact Traveling Wave Solutions for the System of Shallow Water Wave Equations and Modified Liouville Equation Using Extended Jacobian Elliptic Function Expansion Method. American Journal of Computational Mathematics (AJCM) Vol. 4 No. 5 2014.
  24. S. Liu, Z. Fu, Q. Zhao, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Phys. Lett. A 289 (2001) 69-74.
  25. X. Q. Zhao, H. Y. Zhi, H. Q. Zhang, Improved Jacobi-function method with symbolic com¬putation to construct new double-periodic solutions for the generalized Ito system, Chaos Solitons Fractals, 28 (2006) 112-126.
  26. M. Aguero, M. Najera and M. Carrillo, Non classic solitonic structures in DNA's vibrational dynamics, Int. J. Modern Phys. B, 22(2008), 2571-2582.
  27. G. Gaeta, Results and limitations of the soliton theory of DNA transcription, J. Biol. Phys. , 24(1999), 81-96. G. Gaeta, C. Reiss, M. peyrard and T. Dauxois, Simple models of nonlinear DNA
  28. G. Gaeta, C. Reiss, M. Peyrard and T. Dauxois, Simple models of nonlinear DNA dynamics, Rivista del Nuovo cimento, 17(1994), 1-48.
Index Terms

Computer Science
Information Sciences

Keywords

The exp ((-?(?))-expansion method The space-time nonlinear fractional PKP equation The space-time nonlinear fractional SRLW equation The space-time nonlinear frac¬tional STO equation The space-time nonlinear fractional KPP equation Traveling wave solu¬tions Solitary wave solutions Kink-antikink shaped.