Traveling wave solutions of Whitham-Broer-Kaup equations by homotopy perturbation method

Journal of King Saud University - Science

Volumn 22, Issue 3, 2010, Pages 173-176

  Mohyud Din, Syed Tauseef ^a   Yildirim, Ahmet ^b   Demirli, Gülseren ^b  

^a HITEC University Taxila Cantt   (Pakistan)

^b EGE UNIVERSITY   (Turkey)

Author keywords

Blow up solution; Homotopy perturbation method; Periodic solution; The Whitham Broer Kaup equation; Traveling wave solution

Indexed keywords

EID: 77954349361     PISSN: 10183647     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jksus.2010.04.008     Document Type: Article

References (26)

1. Ablowitz M.J., Clarkson P.A. Soliton, Nonlinear Evolution Equations and Inverse Scattering 1991, Cambridge University Press, New York.
2. Achouri, T., Omrani, K., in press. Application of the homotopy perturbation method to the modified regularized long wave equation. Numerical Methods for Partial Differential Equations. doi: doi:10.1002/num.20441.
3. Babolian, E., Azizi, A., Saeidian, J., in press. Some notes on using the homotopy perturbation method for solving time-dependent differential equations. Mathematical and Computer Modelling.
4. Cox D., et al. Ideal, Varieties and Algorithms 1991, Springer, New York.
5. Cveticanin L. Homotopy-perturbation method for pure nonlinear differential equation. Chaos, Solitons and Fractals 2006, 30:1221-1230.
6. El-Sayed S.M., Kaya D. Exact and numerical traveling wave solutions of Whitham-Broer-Kaup equations. Applied Mathematics and Computation 2005, 167:1339-1349.
7. Ghanmi, I., Noomen, K., Omrani, K., in press. Exact solutions for some systems of PDE's by He's homotopy perturbation method. Communication in Numerical Methods in Engineering.
8. He J.H. Homotopy perturbation technique. Computational Methods in Applied Mechanics and Engineering 1999, 178:257-262.
9. He J.H. A coupling method of a homotopy technique and a perturbation technique for non-linear problems. International Journal of Non-linear Mechanics 2000, 35:37-43.
10. He J.H. Homotopy perturbation method: a new nonlinear analytical technique. Applied Mathematics and Computation 2003, 135:73-79.
11. He J.H. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 2006, 20:1141.
12. He J.H. New interpretation of homotopy perturbation method. International Journal of Modern Physics B 2006, 20:2561.
13. He J.H. An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. International Journal of Modern Physics B 2008, 22:3487.
14. He J.H. Recent development of the homotopy perturbation method. Topological Methods in Nonlinear Analysis 2008, 31:205.
15. Inc, M., in press. He's homotopy perturbation method for solving Korteweg-de Vries Burgers equation with initial condition. Numerical Methods for Partial Differential Equations.
16. Dehghan M., Shakeri F. Solution of a partial differential equation subject to temperature over specification by He's homotopy perturbation method. Physica Scripta 2007, 75:778.
17. Momani, Shaher, Erjaee, G.H., Alnasr, M.H., in press. The modified homotopy perturbation method for solving strongly nonlinear oscillators. Computers and Mathematics with Applications.
18. Shakeri F., Dehghan M. Solution of the delay differential equations via homotopy perturbation method. Mathematical and Computer Modelling 2008, 48:486.
19. Whitham G.B. Proceedings of the Royal Society of London, Series A 1967, 299:6.
20. Whitham G.B. Linear and Nonlinear Waves 1974, John Wiley, New York.
21. Xie F., Yan Z., Zhang H. Physics Letters A 2001, 285:76.
22. Yi{dotless}ldi{dotless}ri{dotless}m A. Solution of BVPs for fourth-order integro-differential equations by using homotopy perturbation method. Computers and Mathematics with Applications 2008, 56:3175-3180.
23. Yi{dotless}ldi{dotless}ri{dotless}m A. The homotopy perturbation method for approximate solution of the modified KdV equation. Zeitschrift für Naturforschung A, A Journal of Physical Sciences 2008, 63a:621.
24. Yi{dotless}ldi{dotless}ri{dotless}m, A., in press-a. He's homotopy perturbation method for nonlinear differential-difference equations. International Journal of Computer Mathematics.
25. Yi{dotless}ldi{dotless}ri{dotless}m, A., in press-b. Application of the homotopy perturbation method for the Fokker-Planck equation. Communications in Numerical Methods in Engineering.
26. Zhu, Shun-dong, Chu, Yu-ming, Qiu, Song-liang, in press. The homotopy perturbation method for discontinued problems arising in nanotechnology. Computers and Mathematics with Applications.