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Reseach Article

The Tanh Methods for the Hirota Equations

by Kamal Raslan, Zain F. Abu Shaeer
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 107 - Number 11
Year of Publication: 2014
Authors: Kamal Raslan, Zain F. Abu Shaeer
10.5120/18793-0134

Kamal Raslan, Zain F. Abu Shaeer . The Tanh Methods for the Hirota Equations. International Journal of Computer Applications. 107, 11 ( December 2014), 5-9. DOI=10.5120/18793-0134

@article{ 10.5120/18793-0134,
author = { Kamal Raslan, Zain F. Abu Shaeer },
title = { The Tanh Methods for the Hirota Equations },
journal = { International Journal of Computer Applications },
issue_date = { December 2014 },
volume = { 107 },
number = { 11 },
month = { December },
year = { 2014 },
issn = { 0975-8887 },
pages = { 5-9 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume107/number11/18793-0134/ },
doi = { 10.5120/18793-0134 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:40:46.537222+05:30
%A Kamal Raslan
%A Zain F. Abu Shaeer
%T The Tanh Methods for the Hirota Equations
%J International Journal of Computer Applications
%@ 0975-8887
%V 107
%N 11
%P 5-9
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper we applied the tanh method for analytic study of the nonlinear equations of partial differential equations(PDEs). The proposed method gives more general exact traveling wave solutions without much extra effort. Three applications from literature of nonlinear equation of PDEs were solved by the method. The calculations demonstrate the effectiveness and convenience of the method for nonlinear sub system of PDEs.

References
  1. Abdul-Majid Wazwaz. 2008 . Solitary wave solutions of the generalized shallow water wave (GSWW) equation by Hirota's method, tanh–coth method and Exp-Function method, Appl. Math. Comput. 202 275–286.
  2. Khater, A. H. , Malfiet, W. , Callebaut, D. K. , Kamel, E. S. 2002,The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction–diffusion equations. Chaos Solitons Fractals 14, 513–522
  3. Evans, D. J. , Raslan, K. R. (2005), The tanh function method for solving some important nonlinear partial differential equation. Int. J. Comput. Math. 82(7), 897–905
  4. Fan, E. 2000, Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277, 212–218
  5. Elwakil, S. A. , El-Labany, S. K. , Zahran, M. A. , Sabry, R. 2002, Modified extended tanh-function method for solving nonlinear partial differential equations. Phys. Lett. A 299, 179–188
  6. Gao, Y. T. , Tian, B. 2001, Generalized hyperbolic-function method with computerized symbolic computation to construct the solitonic solutions to nonlinear equations of mathematical physics. Comput. Phys. Commun. 133, 158–164
  7. Tian, B. , Gao, Y. T. 2002 Observable solitonic features of the generalized reaction diffusion model. Z Naturforsch. A 57,39–44
  8. W. Malfliet, 1992,Solitary wave solutions of nonlinear wave equations, Am. J. Phys. (60)650–654.
  9. Abdul-Majid Wazwaz,2006,Exact and explicit travelling wave solutions for the nonlinear Drinfeld Sokolov system,Comm. Nonlinear Sci. Num. Siml. 11(3):311–325.
  10. Abdul-Majid Wazwaz, (2006),Two reliable methods for solving variants of the KdV equation with compact and non-compact structures, Chaos Solitons Fract. 28(2)454–462.
  11. Abdul-Majid Wazwaz,2006,The tanh method for compact and non-compact solutions for variants of the KdV–Burger equations, Phys. D: Nonlinear Phenomena 213 (2) 147–151.
  12. Hoseini,S. M. and Marchant, T. R. , 2006 Solitary wave interaction and evolution for higher-order Hirota equation, Wave Motion. 44, pp. 92-106,
  13. WANG Q, CHEN Yong, LI Biao and ZHANG Hong- Qing,2004,New exact travelling wave Solutions to Hirota equation and (1+1)-dimensional dispersive long wave equation Theor. Phys. (Beijing, China) (41 ). 821–828
  14. Ismail M S and Taha T R 2007 Math. Comput. Simul. 74 302
Index Terms

Computer Science
Information Sciences

Keywords

Tanh method Hirota equations exact solutions.