Application of homotopy perturbation method to solve combined Korteweg de Vries-Modified Korteweg de Vries equation

Journal of Applied Sciences

Volumn 9, Issue 19, 2009, Pages 3587-3592

  Mirgolbabaei, H ^a   Ganji, D D ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b BABOL NOSHIRVANI UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

De Vries equation; De Vries Modified Korteweg; Homotopy perturbation method; Solitary wave solution; The combined Korteweg

Indexed keywords

DE VRIES; DE VRIES-MODIFIED KORTEWEG; HOMOTOPY PERTURBATION METHOD (HPM); SOLITARY WAVE SOLUTION; THE COMBINED KORTEWEG;

TECHNOLOGY;

SOLITONS;

EID: 70349617236     PISSN: 18125654     EISSN: 18125662     Source Type: Journal    
DOI: 10.3923/jas.2009.3587.3592     Document Type: Article

References (35)

1. Abbasbandy, S., 2006a. Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method. Applied Math, Comput., 172: 485-490.
2. Abbasbandy, S., 2006b. Iterated He's homotopy perturbation method for quadratic Riccati differential equation. Appl. Math. Comput, 175: 581-589.
3. Abdou, M.A. and A.A. Soliman, 2005. Variational iteration method for solving Burger's and coupled Burger's equation. J. Comput. Applied Math., 181: 245-251.
4. Al-Hayani, W. and L. Casasus, 2005. Approximate analytical solution of fourth order boundary value problems. Numer. Algorithms, 40: 67-78.
5. Berberler, M.E. and A. Yildiiim, 2009. Hes homotopy perturbation method for solving the shock wave equation. Appl. Anal., (In Press).
6. Biazar, J., E. Babolian and R. Islam, 2004. Solution of the system of ordinary differential equations by adomian decomposition method. Applied Math. Comput, 147: 713-719.
7. Fan, E., 2003. Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics. Chaos Solitons Fractals, 16: 819-839.
8. Ganji, D.D., 2006. The application of Hes homotopy perturbation method to nonlinear equations arising in heat transfer. Phys. Lett. A, 355: 337-341.
9. Ganji, D.D. and A. Rajabi, 2006. Assessment of homotopy-perturbation and perturbation methods in heat radiation equations. Int. Commun. Heat Mass Transfer, 33: 391-400.
10. Ganji, D.D. and A. Sadighi, 2006. Application of he's homotopy-prturbation method to nonlinear coupled systems of reaction-diffusion equations. Int. J. Nonl. Sci. Num. Simu.,7: 411-418.
11. Ganji, D.D., H. Mirgolbabaei, Me. Miansari and Mo. Miansari, 2008. Application of homotopy perturbation method to solve linear and non-linear systems of ordinary differential equations and differential equation of order three. J. Applied Sci., 8: 1256-1261.
12. Hayat, T., M. Khan and S. Asghar, 2004. Homotopy analysis of MHD flows of an Oldroyd 8-constant fluid. ActaMech., 168: 213-32.
13. He, J.H., 1998. Approximate analytical solution for seepage flow with fractional derivatives in porous media. J. Comput. Math. Applied Mech Eng., 167: 57-68.
14. He, J.H., 1999a. Homotopy perturbation technique. J. Comput. Math. Appl. Mech. Eng., 17: 257-262.
15. He, J.H., 1999b. Variational iteration method-a kind of nonlinear analytical technique: Some examples. Int. J. Nonlinear Mech, 34: 699-708.
16. He, J.H., 2000a. A coupling method of homotopy technique and perturbation technique for nonlinear problems. Int. J. Non-Linear Mech., 351: 37-43.
17. He, J.H., 2000b. Variational iteration method for autonomous ordinary differential systems. Applied Math. Comput, 114: 115-123.
18. He, J.H., 2004. The homotopy perturbation method for nonlinear oscillators with discontinuities. Applied Math. Comput, 151: 287-292.
19. He, J.H., 2005a. Application of homotopy perturbation method to nonlinear wave equations. Chaos Solitons Fractals, 26: 695-700.
20. He, J.H., 2005b. Periodic solutions and bifurcations of delay-differential equations. Phys. Lett. A., 347: 228-230.
21. He, J.H., 2006a. Homotopy perturbation method for solving boundary value problems. Phys. Lett. A, 350: 87-88.
22. He, J.H., 2006b. New Interpretation of homotopy perturbation method. Int. J. Modern Phys. B, 20: 2561-2568.
23. He, Ji-H., 2006c. Some asymptotic methods for strongly nonlinear equations. Int. J. Modern Phys. B., 20: 1141-1199.
24. Hong, W.P., 2000. New types of solitary-wave solutions from the combined KdV-MKdV equation. NUOVOCIMENTOB, 115: 117-118.
25. Kocak, H. and A. Yildmm, 2009. Numerical solution of 3D Greens function for the dynamic system of anisotropic elasticity. Phys. Lett. A, 373: 3145-3150.
26. Mirgolbabaei, H., D.D. Ganji and H. Taherian, 2009a. Soliton solution of the Kadomtse-Perviashvili equation by homotopy perturbation method. World J. Modell. Simulat, 5: 38-44.
27. Mirgolbabaei, H., D.D. Ganji, M.M. Etghani and A. Sobati, 2009b. Adapted variational iteration method and axisymmetric flow over a stretching sheet. World J. Modell. Simulat, (In Press).
28. Mohamad, M.N.B., 1992. Exact solutions to the combined KdV and MKdV equation. Math. Meth. Applied Sci., 15: 73-78.
29. Omidvar, M., A. Barari, H. Mirgolbabaei and D.D. Ganji, 2009. Solution of diffusion equations using homotopy perturbation and variational iteration methods. MOEJInt. J. Sci. Technol, (In Press).
30. Rafei, M., D.D. Ganji, H. Daniaha and H. Pashaei, 2007. The variational iteration method for nonlinear oscillators with discontinuities. J. Sound Vibration, 305: 614-620.
31. Siddiqui, A.M., R. Mahmood and Q.K. Ghon, 2006. Thin film flow of a third grade fluid on a moving belt by Hes homotopy perturbation method. Int. J. Nonlin. Sci. Numer. Simulat, 7: 7-14.
32. Sweilam, N.H. and M.M. Khader, 2007. Variational iteration method for one dimensional nonlinear thermoelasticity. Chaos Solitons Fract, 32: 145-149.
33. Wazwaz, A.M., 2006. The variational iteration method for rational solutions for KdV, K(2, 2), Burgers and cubic Boussinesq equations. J. Comput. Applied Math., 207: 18-23.
34. Yu, J., 2000. Exact solitary wave solutions to a combined KdV and MKdV equation. Math. Meth. Applied Sci., 23: 1667-1670.
35. Zhang, L.N. and J.H. He, 2006. Homotopy perturbation method for the solution of the electrostatic potential differential equation. Math. Problems Eng., 2006: 1-6.