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ISRN Mathematical Physics
Volume 2013 (2013), Article ID 146704, 5 pages
The Modified Simple Equation Method for Exact and Solitary Wave Solutions of Nonlinear Evolution Equation: The GZK-BBM Equation and Right-Handed Noncommutative Burgers Equations
1Department of Mathematics, Pabna Science and Technology University, Pabna 6600, Bangladesh
2Department of Applied Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh
3School of Mathematical Sciences, Universiti Sains Malaysia, 11800 USM Pulau Pinang, Malaysia
Received 25 November 2012; Accepted 10 January 2013
Academic Editors: A. Herrera-Aguilar, W.-H. Steeb, and H. Zhou
Copyright © 2013 Kamruzzaman Khan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- J. H. He and X. H. Wu, “Exp-function method for nonlinear wave equations,” Chaos, Solitons & Fractals, vol. 30, no. 3, pp. 700–708, 2006.
- M. A. Akbar and N. H. M. Ali, “Exp-function method for duffing equation and new solutions of () dimensional dispersive long Wave Equations,” Progress in Applied Mathematics, vol. 1, no. 2, pp. 30–42, 2011.
- H. Naher, F. A. Abdullah, and M. Ali Akbar, “New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the exp-function method,” Journal of Applied Mathematics, Article ID 575387, 14 pages, 2012.
- H. Naher, A. F. Abdullah, and M. A. Akbar, “The Exp-function method for new exact solutions of the nonlinear partial differential equations,” International Journal of the Physical Sciences, vol. 6, no. 29, pp. 6706–6716, 2011.
- M. A. Abdou, “The extended tanh method and its applications for solving nonlinear physical models,” Applied Mathematics and Computation, vol. 190, no. 1, pp. 988–996, 2007.
- E. Fan, “Extended tanh-function method and its applications to nonlinear equations,” Physics Letters A, vol. 277, no. 4-5, pp. 212–218, 2000.
- M. L. Wang, “Solitary wave solutions for variant Boussinesq equations,” Physics Letters A, vol. 199, no. 3-4, pp. 169–172, 1995.
- E. M. E. Zayed, H. A. Zedan, and K. A. Gepreel, “On the solitary wave solutions for nonlinear Hirota-Satsuma coupled KdV of equations,” Chaos, Solitons & Fractals, vol. 22, no. 2, pp. 285–303, 2004.
- M. Wang, X. Li, and J. Zhang, “The -expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,” Physics Letters A, vol. 372, no. 4, pp. 417–423, 2008.
- E. M. E. Zayed and K. A. Gepreel, “The -expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics,” Journal of Mathematical Physics, vol. 50, no. 1, pp. 013502–013514, 2009.
- E. M. E. Zayed, “Traveling wave solutions for higher dimensional nonlinear evolution equations using the -expansion method,” Journal of Applied Mathematics & Informatics, vol. 28, pp. 383–395, 2010.
- M. A. Akbar, N. H. M. Ali, and E. M. E. Zayed, “A generalized and improved -expansion method for nonlinear evolution equations,” Mathematical Problems in Engineering, vol. 2012, Article ID 459879, 22 pages, 2012.
- M. Ali Akbar, N. Hj. Mohd. Ali, and E. M. E. Zayed, “Abundant exact traveling wave solutions of generalized Bretherton equation via -expansion method,” Communications in Theoretical Physics, vol. 57, no. 2, pp. 173–178, 2012.
- M. A. Akbar, N. H. M. Ali, and S. T. Mohyud-Din, “The alternative -expansion method with generalized Riccati equation: application to fifth order ()-dimensional Caudrey-Dodd-Gibbon equation,” International Journal of Physical Sciences, vol. 7, no. 5, pp. 743–752, 2012.
- M. A. Akbar and N. H. M. Ali, “The alternative -expansion method and its applications to nonlinear partial differential equations,” International Journal of Physical Sciences, vol. 6, no. 35, pp. 7910–7920, 2011.
- M. A. Akbar, N. H. M. Ali, and S. T. Mohyud-Din, “Some new exact traveling wave solutions to the ()-dimensional Kadomtsev-Petviashvili equation,” World Applied Sciences Journal, vol. 16, no. 11, pp. 1551–1558, 2012.
- R. Hirota, “Exact envelope-soliton solutions of a nonlinear wave equation,” Journal of Mathematical Physics, vol. 14, pp. 805–809, 1973.
- R. Hirota and J. Satsuma, “Soliton solutions of a coupled Korteweg-de Vries equation,” Physics Letters A, vol. 85, no. 8-9, pp. 407–408, 1981.
- M. R. Miura, Backlund Transformation, Springer, Berlin, Germany, 1978.
- M. J. Ablowitz and P. A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering, vol. 149 of London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, UK, 1991.
- D. Lu and Q. Shi, “New Jacobi elliptic functions solutions for the combined KdV-MKdV equation,” International Journal of Nonlinear Science, vol. 10, no. 3, pp. 320–325, 2010.
- A. J. M. Jawad, M. D. Petković, and A. Biswas, “Modified simple equation method for nonlinear evolution equations,” Applied Mathematics and Computation, vol. 217, no. 2, pp. 869–877, 2010.
- E. M. E. Zayed, “A note on the modified simple equation method applied to Sharma-Tasso-Olver equation,” Applied Mathematics and Computation, vol. 218, no. 7, pp. 3962–3964, 2011.
- E. M. E. Zayed and S. A. H. Ibrahim, “Exact solutions of nonlinear evolution equations in mathematical physics using the modified simple equation method,” Chinese Physics Letters, vol. 29, no. 6, Article ID 060201, 2012.