Traveling wave solutions of seventh-order generalized KdV equations using he's polynomials

International Journal of Nonlinear Sciences and Numerical Simulation

Volumn 10, Issue 2, 2009, Pages 227-233

  Mohyud Din, S Tauseef ^a   Noor, Muhammad Aslam ^a   Noor, Khalida Inayat ^a  

^a Department of Electrical Computer Engineering   (Pakistan)

Author keywords

He's polynomials; Seventh order KdVs; Variational iteration method

Indexed keywords

EID: 65349085836     PISSN: 15651339     EISSN: None     Source Type: Journal    
DOI: 10.1515/IJNSNS.2009.10.2.227     Document Type: Article

References (27)

1. B. R. Duffy and E. J. Parkes, Traveling solitary wave solutions to a seventh order generalized KdV equation, Phys. Lett. A, 214 (1996), 271-272.
2. A. Ghorbani and J. S. Nadjfi, He's homotopy perturbation method for calculating Adomian's polynomials, Int. J. Nonlin. Sci. Num. Simul., 8 (2) (2007), 229-332.
3. A. Ghorbani, Beyond Adomian's polynomials: He polynomials, Chaos, Solitons & Fractals, (2007), in press.
4. J. H. He, Some asymptotic methods for strongly nonlinear equation, Int. J. Mod. Phys., 20(2006), 1144-1199.
5. J. H. He, Homotopy perturbation method for solving boundary value problems, Phys. Lett. A, 350 (2006), 87-88.
6. J. H. He, Comparison of homotopy perturbation method and homotopy analysis method, Appl. Math. Comput. 156 (2004), 527-539.
7. J. H. He, Homotopy perturbation method for bifurcation of nonlinear problems, Int. J. Nonlin. Sci. Numer. Simul. 6 (2) (2005), 207-208.
8. J. H. He, The homotopy perturbation method for nonlinear oscillators with discontinuities, Appl. Math. Comput. 151 (2004), 287-292.
9. J. H. He, A coupling method of homotopy technique and perturbation technique for nonlinear problems, Int. J. Nonlin. Mech, 35 (1)(2000), 115-123.
10. J. H. He, An elementary introduction of recently developed asymptotic methods and nanomechanics in textile engineering, Int. J. Mod. Phys. B 22 (21) (2008), 3487-4578.
11. J. H. He, Recent developments of the homotopy perturbation method, Top. Meth. Nonlin. Anal. 31(2008), 205-209.
12. D. Kaya, An explicit and numerical solution of some fifth-order KdV equation by decomposition method, Appl. Math. Comput 144 (2003), 533-363.
13. D. Kaya and Salah M. El-Sayed, An application of the decomposition method for generalized KdV and RLW equations, Chaos, Solitons & Fractals, 17 (2003), 869-877.
14. W. Ma, Travelling wave solutions to a seventh order generalized KdV equation, Phys. Lett. A, 180 (1993), 221-224.
15. S. T. Mohyud-Din and M. A. Noor, Homotopy perturbation method for solving fourth-order boundary value problems, Math. Prob. Engg. (2007), 1-15, Article ID 98602, doi:10.1155/2007/98602.
16. M. A. Noor and S. T. Mohyud-Din, Homotopy perturbation method for nonlinear higher-order boundary value problems, Int. J. Nonlin. Sci. Num. Simul, 9(4) (2008), 395-408.
17. M. A. Noor and S. T. Mohyud-Din, An efficient algorithm for solving fifth order boundary value problems, Math. Comput. Modl. 45 (2007), 954-964.
18. M. A. Noor and S. T. Mohyud-Din, Homotopy perturbation method for solving sixth-order boundary value problems, Comput. Math. Appl., 55 (12) (2008), 2953-2972.
19. M. A. Noor and S. T. Mohyud-Din, Variational iteration method for solving higher-order nonlinear boundary value problems using He's polynomials, Int. J. Nonlin. Sci. Num. Sim., 9 (2) (2008), 141-157.
20. M. A. Noor and S. T. Mohyud-Din, Variational iteration method for solving fifth-order boundary value problems using He's polynomials, Math. Prob. Engg. (2008), Article ID 954794, doi: 10:1155/2008/954794.
21. M. A. Noor and S. T. Mohyud-Din, Modified variational iteration method for heat and wave-like equations, Acta Applnda. Mathmtce. (2008), DOI: 10. 1007/s 10440-008-9255-x.
22. M. A. Noor and S. T. Mohyud-Din, Modified variational iteration method for solving fourth-order boundary value problems, J. Appl. Math. Comput. (2008), Article ID: 90, DOI: 10. 1007/s 12190-008-0090-z.
23. M. A. Noor and S. T. Mohyud-Din, Variational homotopy perturbation method for solving higher dimensional initial boundary value problems, Math. Prob. Engg. (2008), Article ID 696734, doi:10.1155/2008/696734.
24. M. A. Noor and S. T. Mohyud-Din, Variational iteration method for unsteady flow of gas through a porous medium using He's polynomials and Pade approximants, Comput. Math. Appl. (2008).
25. M. A. Noor and S. T. Mohyud-Din, Modified variational iteration method for solving Helmholte equations, Comput. Math. Modlg. (2008).
26. M. A. Noor and S. T. Mohyud-Din, Variational iteration method for solving twelfth-order boundary value problems using He's polynomials, Comput. Math. Modlg. (2008).
27. L. Xu, He's homotopy perturbation method for a boundary layer equation in unbounded domain, Comput. Math. Appl., 54 (2007), 1067-1070.