Traveling Wave Solutions of The (1+1)-Dimensional Compound KdVB equation by Exp -Expansion Method
the exp(âˆ'Φ(η)) -expansion method, complixiton soliton solutions, the (1+1)- dimensional compound kdvb equations, traveling wave solutions, nonline, the exp(−Φ(η)) -expansion method
Abstract
In this article, we apply the exp ( Φ(η))-expansion method for seeking the exact solutions of NLEEs via the (1+1)-Dimensional Compound KdvB equation. Plentiful traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, trigonometric, and rational functions. The obtained results show that exp(-Φ(η))-expansion method is very powerful and concise mathematical tool for nonlinear evolution equations in science and engineering.
Downloads
How to Cite
References
A-M Wazwaz (2004) A sine-cosine method for handlingnonlinear wave equations. 40(5-6), 499-508. https://doi.org/10.1016/j.mcm.2003.12.010
Fan (2000) Extended tanh-function method and its applications to nonlinear equations. 277(4-5), 212-218. https://doi.org/10.1016/s0375-9601(00)00725-8
E. Fan (2000) Two new applications of the homogeneous balance method. 265, 353-357.
A. Wazwaz, Burgers- equations (2005) The tanh method for generalized forms of nonlinear heat conduction and Burgers- Fisher equations. 169, 321-338.
M. Usman, A. Nazir, T. Zubair, I. Rashid, Z. Naheed, S. Mohyud-Din (2013) Solitary wave solutions of (3+1)- dimensional Jimbo Miwa and Pochhammer-Chree equations by modified Exp-function method. (1), 27-36.
Ji-Huan He, Xu-Hong Wu (2006) Exp-function method for nonlinear wave equations. 30(3), 700-708. https://doi.org/10.1016/j.chaos.2006.03.020
M. Akbar, N. Ali (2012) New Solitary and Periodic Solutions of Nonlinear Evolution Equation by Exp-function Method. (12), 1603-1610.
Zhenya Yan, Hongqing Zhang (2001) New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water. 285(5-6), 355-362. https://doi.org/10.1016/s0375-9601(01)00376-0
D. Liu (2005) Jacobi elliptic function solutions for two variant Boussinesq equations. 24, 1373-1385.
Y. Chen, Q. Wang, Chaos Fractals (2005) Extended Jacobi elliptic function rational expansion method and abundant families of Jacobi elliptic functions solutions to (1+1)-dimensional dispersive long wave equation. 24, 745-57.
A. Wazwaz (2012) Multiple-soliton solutions for a (3+1)- dimensional generalized KP equation. 17, 491-495.
H. Roshid, N. Rahman, M. Akbar (2013) Traveling wave solutions of nonlinear Klein- Gordon equation by extended (G/G) -expansion method. 3(1), 10-16.
M. Wang, X. Li, J. Zhang, The method, Phys. A (2008) The (G´/G) - expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. 372, 417-423.
A. Bekir (2008) Application of the (G´/G) -expansion method for nonlinear evolution equations. 372, 3400-3406.
H. Roshid, M. Alam, M. Hoque, M. Akbar (2013) A new extended (G´/G) - expansion method to find exact traveling wave solutions of nonlinear evolution equations, mathematics and Statistics. 1(3), 162-166. https://doi.org/10.13189/ms.2013.010308
S. Zhang, J. Tong, W. Wang, Phys. A (2008) A generalized (G´/G) -expansion method for the mKdV equation with variable coefficients. 372, 2254-2257.
M. Akbar, N. Ali, A. E.M.E. Zayed, Math. Engr (2012) A generalized and improved (G´/G) - expansion method for nonlinear evolution equations. 2012, 22. https://doi.org/10.1155/2012/459879
Md. Alam, Md. Akbar, Syed Mohyud-Din (2014) A novel (G′/G)-expansion method and its application to the Boussinesq equation. 23(2), 020203. https://doi.org/10.1088/1674-1056/23/2/020203
M. Alam, M. Akbar (2014) Traveling wave solutions of the nonlinear (1+1)- dimensional modified Benjamin-Bona-Mahony equation by using novel (G´/G) - expansion. 4(1), 147-165.
A. Jawad, M. Petkovic, A. Biswas (2010) Modified simple equation method for nonlinear evolution equations. 217, 869-877.
K. Khan, M. Akbar, M. Alam (2013) Traveling wave solutions of the nonlinear Drinfel'd-Sokolov-Wilson equation and modified Benjamin-Bona-Mahony equations. 21, 233-240. https://doi.org/10.1016/j.joems.2013.04.010
J. Zhang, F. Jiang, X. Zhao, Int. Math (2010) An improved (G´/G) -expansion method for solving nonlinear evolution equations. 87(8), 1716-1725.
M. Ablowitz, P. Clarkson (1991) Soliton.
D. Liu (2005) Jacobi elliptic function solutions for two variant Boussinesq equations. 24, 1373-85.
Hasibun Naher, Farah Abdullah (2013) New approach of (G´/G) -expansion method and new approach of generalized (G´/G) -expansion method for nonlinear evolution equation, AIP Advances 3, 032116 (2013). 3(3), 32116. https://doi.org/10.1063/1.4794947
M. Alam, M. Akbar, K. Khan (2013) Some new exact traveling wave solutions to the (2+1)- dimensional breaking soliton equation. 25(3), 500-523.
Md Alam, M. Akbar (2013) Exact traveling wave solutions of the KP-BBM equation by using the new approach of generalized (G′/G)-expansion method. 2(1), 617. https://doi.org/10.1186/2193-1801-2-617
Md. Alam, M. Akbar (2013) Traveling Wave Solutions of Nonlinear Evolution Equations Via the New Generalized (G′/G)-Expansion Method. 1(4), 129-136. https://doi.org/10.13189/ujcmj.2013.010403
M. Alam, M. Akbar, H. Roshid (2013) Study of nonlinear evolution equations to construct traveling wave solutions via the new approach of generalized (G´/G) - expansion method. 1(3), 102-112. https://doi.org/10.13189/ms.2013.010302
M. Zhao, C. Li The exp(−Φ(η))-expansion method applied to nonlinear evolution equations, Paper. http://www.paper.edu.cn
R. Islam, M. Alam, A. Hossain, H. Roshid, M. Akbar (2013) traveling wave solutions of nonlinear evolution equations via exp (-Φ(η)) -expansion method. 13(11), XXX-XXX.
Published
2013-11-28
Issue
Section
License
Copyright (c) 2013 Authors and Global Journals Private Limited

This work is licensed under a Creative Commons Attribution 4.0 International License.