Journal Menu

- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents

ISRN Mathematical Physics

Volume 2013 (2013), Article ID 146704, 5 pages

http://dx.doi.org/10.1155/2013/146704

Research Article

## 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

^{1}Department of Mathematics, Pabna Science and Technology University, Pabna 6600, Bangladesh^{2}Department of Applied Mathematics, University of Rajshahi, Rajshahi 6205, Bangladesh^{3}School 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.

#### Linked References

- 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. A. Akbar and N. H. M. Ali, “Exp-function method for duffing equation and new solutions of ($2+1$) dimensional dispersive long Wave Equations,”
*Progress in Applied Mathematics*, vol. 1, no. 2, pp. 30–42, 2011. View at Google Scholar - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - 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. View at Google Scholar - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - E. Fan, “Extended tanh-function method and its applications to nonlinear equations,”
*Physics Letters A*, vol. 277, no. 4-5, pp. 212–218, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - M. L. Wang, “Solitary wave solutions for variant Boussinesq equations,”
*Physics Letters A*, vol. 199, no. 3-4, pp. 169–172, 1995. View at Publisher · View at Google Scholar · View at MathSciNet - 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. View at Publisher · View at Google Scholar · View at MathSciNet - M. Wang, X. Li, and J. Zhang, “The $({G}^{\text{'}}/G)$-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,”
*Physics Letters A*, vol. 372, no. 4, pp. 417–423, 2008. View at Publisher · View at Google Scholar · View at MathSciNet - E. M. E. Zayed and K. A. Gepreel, “The $({G}^{\text{'}}/G)$-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. View at Publisher · View at Google Scholar · View at MathSciNet - E. M. E. Zayed, “Traveling wave solutions for higher dimensional nonlinear evolution equations using the $({G}^{\text{'}}/G)$-expansion method,”
*Journal of Applied Mathematics & Informatics*, vol. 28, pp. 383–395, 2010. View at Google Scholar - M. A. Akbar, N. H. M. Ali, and E. M. E. Zayed, “A generalized and improved $({G}^{\text{'}}/G)$-expansion method for nonlinear evolution equations,”
*Mathematical Problems in Engineering*, vol. 2012, Article ID 459879, 22 pages, 2012. View at Publisher · View at Google Scholar - M. Ali Akbar, N. Hj. Mohd. Ali, and E. M. E. Zayed, “Abundant exact traveling wave solutions of generalized Bretherton equation via $({G}^{\text{'}}/G)$-expansion method,”
*Communications in Theoretical Physics*, vol. 57, no. 2, pp. 173–178, 2012. View at Publisher · View at Google Scholar · View at MathSciNet - M. A. Akbar, N. H. M. Ali, and S. T. Mohyud-Din, “The alternative $({G}^{\text{'}}/G)$-expansion method with generalized Riccati equation: application to fifth order ($1+1$)-dimensional Caudrey-Dodd-Gibbon equation,”
*International Journal of Physical Sciences*, vol. 7, no. 5, pp. 743–752, 2012. View at Google Scholar - M. A. Akbar and N. H. M. Ali, “The alternative $({G}^{\text{'}}/G)$-expansion method and its applications to nonlinear partial differential equations,”
*International Journal of Physical Sciences*, vol. 6, no. 35, pp. 7910–7920, 2011. View at Google Scholar - M. A. Akbar, N. H. M. Ali, and S. T. Mohyud-Din, “Some new exact traveling wave solutions to the ($3+1$)-dimensional Kadomtsev-Petviashvili equation,”
*World Applied Sciences Journal*, vol. 16, no. 11, pp. 1551–1558, 2012. View at Google Scholar - R. Hirota, “Exact envelope-soliton solutions of a nonlinear wave equation,”
*Journal of Mathematical Physics*, vol. 14, pp. 805–809, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - 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. View at Publisher · View at Google Scholar · View at MathSciNet - 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. View at Publisher · View at Google Scholar · View at MathSciNet - 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. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - 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. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet - 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. View at Publisher · View at Google Scholar