New Exact Traveling Wave Solutions for Some Coupled BBM Equations

Affiliation(s)

Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing, China.

Department of Basic Courses, Beijing Union University, Beijing, China.

Department of Mathematics and Physics, Beijing Institute of Petrochemical Technology, Beijing, China.

Department of Basic Courses, Beijing Union University, Beijing, China.

ABSTRACT

The present paper
deals with results of explicit traveling wave solutions for some coupled BBM
equations. By detailed computation and using the (*G *'/*G*)-expansion method, many traveling wave solutions
are given. These traveling waves are in the form of hyperbolic functions, the
trigonometric functions and the rational functions, which show the reliability
and efficiency of the used method.

Cite this paper

Zhao, Y. and Xu, Q. (2014) New Exact Traveling Wave Solutions for Some Coupled BBM Equations.*Applied Mathematics*, **5**, 1508-1515. doi: 10.4236/am.2014.510144.

Zhao, Y. and Xu, Q. (2014) New Exact Traveling Wave Solutions for Some Coupled BBM Equations.

References

[1] Cui, L.W. and Zhao, Y. (2012) Orbital Stability of Solitary Waves for Coupled BBM Equations. Advances in Mathematics (Chinese), 41, 341-346.

[2] Zhao, Y. and Xu, Q. (to appear) Existence and Instability of Solitary Waves with Nonzero Asymptotic Value for Some BBM Equations.

[3] Wang, M., Li, X. and Zhang, J. (2008) The (G’/G)-Expansion Method and Traveling Wave Solutions of Nonlinear Evolution Equations in Mathematical Physics. Physics Letters A, 372, 417-423.

http://dx.doi.org/10.1016/j.physleta.2007.07.051

[4] Bekir, A. (2008) Application of the (G’/G)-Expansion Method for Nonlinear Evolution Equations. Physics Letters A, 372, 3400-3406.

http://dx.doi.org/10.1016/j.physleta.2008.01.057

[5] Zayed, E.M.E. and Al-Joudi, S. (2010) Application of an Extended (G’/G)-Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics. Mathematical Problems in Engineering, 2010, Article ID: 768573.

[6] Ali Akbar, M., Ali, N.H.M. and Zayed, E.M.E. (2012) A Generalized and Improved (G’/G)-Expansion Method for Nonlinear Evolution Equations. Mathematical Problems in Engineering, 2012, Article ID: 459879.

[7] Taha, W.M., Noorani, M.S.M. and Hashim, I. (2014) New Exact Solutions of Sixth-Order Thin-Film Equation. Journal of King Saud University—Science, 26, 75-78.

[1] Cui, L.W. and Zhao, Y. (2012) Orbital Stability of Solitary Waves for Coupled BBM Equations. Advances in Mathematics (Chinese), 41, 341-346.

[2] Zhao, Y. and Xu, Q. (to appear) Existence and Instability of Solitary Waves with Nonzero Asymptotic Value for Some BBM Equations.

[3] Wang, M., Li, X. and Zhang, J. (2008) The (G’/G)-Expansion Method and Traveling Wave Solutions of Nonlinear Evolution Equations in Mathematical Physics. Physics Letters A, 372, 417-423.

http://dx.doi.org/10.1016/j.physleta.2007.07.051

[4] Bekir, A. (2008) Application of the (G’/G)-Expansion Method for Nonlinear Evolution Equations. Physics Letters A, 372, 3400-3406.

http://dx.doi.org/10.1016/j.physleta.2008.01.057

[5] Zayed, E.M.E. and Al-Joudi, S. (2010) Application of an Extended (G’/G)-Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics. Mathematical Problems in Engineering, 2010, Article ID: 768573.

[6] Ali Akbar, M., Ali, N.H.M. and Zayed, E.M.E. (2012) A Generalized and Improved (G’/G)-Expansion Method for Nonlinear Evolution Equations. Mathematical Problems in Engineering, 2012, Article ID: 459879.

[7] Taha, W.M., Noorani, M.S.M. and Hashim, I. (2014) New Exact Solutions of Sixth-Order Thin-Film Equation. Journal of King Saud University—Science, 26, 75-78.