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New applications of variational iteration method. (English) Zbl 1084.35539
Summary: The variational iteration method is used for solving three types of nonlinear partial differential equations such as coupled Schrödinger-KdV, generalized KdV and shallow water equations. The exact and numerical solutions obtained by the variational iteration method are compared with that obtained using Adomian decomposition method. In this paper, He’s variational iteration method is introduced to overcome the difficulty arising in calculating Adomian polynomials.

35Q53KdV-like (Korteweg-de Vries) equations
35Q35PDEs in connection with fluid mechanics
Full Text: DOI
[1] Drazin, P. G.; Johnson, R. S.: Solutions: an introduction. (1989) · Zbl 0661.35001
[2] Whitham, G. B.: Linear nonlinear waves. (1974) · Zbl 0373.76001
[3] Debtnath, L.: Nonlinear partial differential equations for scientist and engineers. (1997)
[4] Wazwaz, A. M.: Partial differential equations methods and applications. (2002) · Zbl 1079.35001
[5] Hereman, W.; Banerjee, P. P.; Korpel, A.; Assnto, J.; Van Immerzeele, A.; Meerpoel, A.: J. phys. A: math. Gen.. 607 (1986) · Zbl 0621.35080
[6] Lei, Y.; Fajianj, Z.; Yinghai, W.: Chaos solitons fractals. 13, 337 (2002)
[7] Hirota, R.: Phys. rev. Lett.. 27, 1192 (1971)
[8] A. Coely, et al. (Eds.), Backlund and Darboux Transformations, American Mathematical Society, Providence, Rhode Island, 2001.
[9] Malfeit, W.: Am. J. Phys.. 60, 650 (1992)
[10] Yan, C. T.: Phys. lett. A. 224, 77 (1996)
[11] Wang, M. L.: Phys. lett. A. 215, 279 (1996)
[12] Yan, Z. Y.; Zhang, H. Q.: J. phys. A. 34, 1785 (2001)
[13] Yan, Z. Y.; Zhang, H. Q.: Appl. math. Mech.. 21, 382 (2000)
[14] Yan, Z. Y.; Zhang, H. Q.: Phys. lett. A. 285, 355 (2001)
[15] Yan, Z. Y.: Phys. lett. A. 292, 100 (2001)
[16] Kaya, D.: Commun. nonlinear sci. Numer. simul.. 10, No. 6, 693-702 (2005)
[17] Kaya, D.; Elsayed, S. M.: Phys. lett. A.. 313, 82 (2003)
[18] Al-Khalled, K.; Allan, F.: Math. comput. Simul.. 66, No. 6, 479-486 (2004)
[19] He, J. H.: Comput. methods appl. Mech. eng.. 167, 57-68 (1998)
[20] He, J. H.: Comput. methods appl. Mech. eng.. 167, 69-73 (1998)
[21] He, J. H.: Int. J. Nonlinear mech.. 34, 699-708 (1999)
[22] He, J. H.: Commun. nonlinear sci. Numer. simul.. 2, No. 4, 230-235 (1997)
[23] He, J. H.: Appl. math. Comput.. 114, No. 2,3, 115-123 (2000)
[24] Marinca, V.: Int. J. Nonlinear sci. Numer. simul.. 3, 107-120 (2002) · Zbl 1079.34028
[25] Draganescu, Gh.E.; Capalnasan, V.: Int. J. Nonlinear sci. Numer. simul.. 4, 219-226 (2004)
[26] Wazwaz, A. M.: Computer and mathematics with application. 4, 1237-1244 (2001)
[27] He, J. H.: Approximate analytical methods in science and engineering. (2002)
[28] He, J. H.: Generalized variational principles in fluids. (2003) · Zbl 1054.76001
[29] Abdou, M. A.; Soliman, A. A.: Variational iteration method for solving burger’s and coupled burger’s equations. J. comput. Appl. math. 181, No. 2, 245-251 (2005) · Zbl 1072.65127