CFP last date
20 June 2024
Reseach Article

Extended Jacobian Elliptic Function Expansion Method and its Applications for Solving some Nonlinear Evolution Equations in Mathematical Physics

by Maha S. M. Shehata
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 109 - Number 12
Year of Publication: 2015
Authors: Maha S. M. Shehata
10.5120/19237-0621

Maha S. M. Shehata . Extended Jacobian Elliptic Function Expansion Method and its Applications for Solving some Nonlinear Evolution Equations in Mathematical Physics. International Journal of Computer Applications. 109, 12 ( January 2015), 1-4. DOI=10.5120/19237-0621

@article{ 10.5120/19237-0621,
author = { Maha S. M. Shehata },
title = { Extended Jacobian Elliptic Function Expansion Method and its Applications for Solving some Nonlinear Evolution Equations in Mathematical Physics },
journal = { International Journal of Computer Applications },
issue_date = { January 2015 },
volume = { 109 },
number = { 12 },
month = { January },
year = { 2015 },
issn = { 0975-8887 },
pages = { 1-4 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume109/number12/19237-0621/ },
doi = { 10.5120/19237-0621 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:44:34.629938+05:30
%A Maha S. M. Shehata
%T Extended Jacobian Elliptic Function Expansion Method and its Applications for Solving some Nonlinear Evolution Equations in Mathematical Physics
%J International Journal of Computer Applications
%@ 0975-8887
%V 109
%N 12
%P 1-4
%D 2015
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Extended Jacobian elliptic function expansion method is employed to find the ex¬act traveling wave solutions involving parameters for nonlinear evolution equations. When these parameters are taken to be special values, the solitary wave solutions are derived from the exact traveling wave solutions. It is shown that extended Jacobian elliptic func¬tion expansion method provides an effective and a more powerful mathematical tool for solving nonlinear evolution equations in mathematical physics. Comparison between our results and the well-known results will be presented.

References
  1. M. J. Ablowitz, H. Segur, Solitions and Inverse Scattering Transform, SIAM, Philadel¬phia 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 ex-tented 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. M. Wazwaz, A sine-cosine method for handling nonlinear wave equations, Math. Comput. Modelling, 40 (2004) 499-508.
  10. 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. L. Wang, Exct solutions for a compound KdV-Burgers equation, Phys. Lett. A 213 (1996) 279-287.
  13. 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.
  14. Y. J. Ren, H. Q. Zhang, A generalized F-expansion method to find abundant families of Jacobi elliptic function solutions of the (2+l)-dimensional Nizhnik-Novikov-Veselov equation, Chaos Solitons Fractals, 27 (2006) 959-979.
  15. 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.
  16. J. H. He, X. H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fractals 30 (2006) 700-708.
  17. H. Aminikhad, H. Moosaei, M. Hajipour, Exact solutions for nonlinear partial differ¬ential equations via Exp-furictiori method, Numer. Methods Partial Differ. Equations, 26 (2009) 1427-1433.
  18. Z. Y. Zhang, New exact traveling wave solutions for the nonlinear Klein-Gordon equa¬tion, Turk. J. Phys. , 32 (2008) 235-240.
  19. E. H. M. Zahran and Mostafa M. A. khater, Exact solutions to some nonlinear evolution equations by the (G^'/G) -expansion method equations in mathematical physics, Jokull Journal, Vol. 64, No. 5; May 2014.
  20. 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
  21. 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.
  22. E. M. E. Zayed, The (G^'/G)- expansion method and its applications to some nonlinear evolution equations in mathematical physics, J. Appl. Math. Computing, 30 (2009) 89-103.
  23. Q. Dai , J. F. Zhang, Jacobian elliptic function method for nonlinear differential difference equations, Chaos Solutions Fractals, 27 (2006) 1042-1049.
  24. 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.
  25. S. Liu, Z. Fu, S. Liu, Q. Zhao, Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations, Phys. Lett. A 289 (2001) 69-74.
  26. X. Q. Zhao, H. Y. Zhi, H. Q. Zhang, Improved Jacobi-function method with symbolic computation to construct new double-periodic solutions for the generalized Ito system, Chaos Solitons Fractals, 28 (2006) 112-126.
  27. R. Hirota, Y. Ohta, Hierarchies of coupled soliton equations I, J phys. Soc. Jpn. 60. (1991) 798.
  28. S. Zhang, New exact non-traveling wave and coefficient function solutions of the (2+1)-dimensional breaking soliton equations, Phys. Lett. A. 368 (2007) 470.
  29. Y. Cheng, B. Li, Symbolic computation and construction of soliton-like solutions to the (2+l)-dimensional breaking soliton equation, Commun. Theor. Phys. (Beijing, China) 40 (2003) 137.
  30. Y. Z. Peng, New exact solutions for (2+l)-dimensional breaking soliton equation, Commun. Theor. Phys. (Beijing, China) 43 (2005) 205.
  31. Y. Z. Peng, E. V. Krishna, Two classes of new exact solutions to (2+l)-dimensional breaking soliton equation, Commun. Theor. Phys. (Beijing, China) 44 (2005) 807.
  32. F. D. Xie, Y. Zhang, Z. S. Lu, Symbolic computation in non-linear evolution equation: application to (3+1) dimensional Kadomtsev-Petviashvili equation, Chaos, Solitons Fractals 24 (2005) 257.
  33. H. Zhao, C. Bai, New doubly periodic and multiple soliton solutions of the generalized (3+l)-dimensional Kadomtsev-Petviashvilli equation with variable coefficients, Chaos, Solitons Fractals 30 (2006) 217.
  34. Y. Chen, Z. Yan, H. Zhang, New explicit solitary wave solutions for (2+l)-dimensional Boussinesq equation and (3+l)-dimensional KP equation Phys. Lett. A. 307 (2003) 107.
  35. Ahmet Bekir, Ferhat Uygun, Exact traveling wave solutions of nonlinear evolution equations by using the G^'/G expansion method, Arab Journal of Mathematical Sciences 18 (2012) 73-85.
  36. E. H. M. Zahran and Mostafa M. A. khater, The modified simple equation method and its applications for solving some nonlinear evolution equations in mathematical physics, Jokull Journal, Vol. 64, No. 5; May 2014.
Index Terms

Computer Science
Information Sciences

Keywords

Extended Jacobian elliptic function expansion method (2+l)-Dimensional soliton breaking equation (3+l)-Dimensional Kadomstev-Petviash-vili Tarveling wave so¬lutions Solitary wave solutions.