Geodesic
Solution of Davey–Stewartson equations by homotopy perturbation method
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 8, pp. 1451-1457 
H. A. Zedan; S. Sh. Tantawy. Solution of Davey–Stewartson equations by homotopy perturbation method. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 8, pp. 1451-1457. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a7/
@article{ZVMMF_2009_49_8_a7,
     author = {H. A. Zedan and S. Sh. Tantawy},
     title = {Solution of {Davey{\textendash}Stewartson} equations by homotopy perturbation method},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1451--1457},
     year = {2009},
     volume = {49},
     number = {8},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a7/}
}
TY  - JOUR
AU  - H. A. Zedan
AU  - S. Sh. Tantawy
TI  - Solution of Davey–Stewartson equations by homotopy perturbation method
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 1451
EP  - 1457
VL  - 49
IS  - 8
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a7/
LA  - en
ID  - ZVMMF_2009_49_8_a7
ER  - 
%0 Journal Article
%A H. A. Zedan
%A S. Sh. Tantawy
%T Solution of Davey–Stewartson equations by homotopy perturbation method
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 1451-1457
%V 49
%N 8
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_8_a7/
%G en
%F ZVMMF_2009_49_8_a7

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, we extend the homotopy perturbation method to solve the Davey–Stewartson equations. The homotopy perturbation method is employed to compute an approximation to the solution of the equations. Computation the absolute errors between the exact solutions of the Davey–Stewartson equations and the HPM solutions are presented. Some plots are given to show the simplicity the method.

[1] He J. H., “Homotopy perturbation technique”, Comput. Meth. Appl. Mech. Engng., 178 (1999), 257–262 | DOI | MR | Zbl

[2] Cveticanin L., “Homotopy perturbation method for pure nonlinear differential equation”, Chaos, Solitons and Fractals, 30 (2006), 1221–1230 | DOI | Zbl

[3] El-Shahed M., “Application of He's homotopy perturbation method to Volterra's integro-differential equation”, Int. J. Nonlinear Sei. Numer. Simul., 6:2 (2005), 163–168 | MR

[4] He J. H., “Asymptotology by homotopy perturbation method”, Appl. Math. Comput., 156 (2004), 591–596 | DOI | MR | Zbl

[5] He J. H., “The homotopy perturbation method for nonlinear oscillators with discontinuities”, Appl. Math. Comput., 151 (2004), 287–292 | DOI | MR | Zbl

[6] He J. H., “Applicaton of the homotopy perturbaton method to nonlinear wave equations”, Chaos, Solitons and Fractals, 26 (2005), 695–700 | DOI | Zbl

[7] He J. H., “Comparison of homotopy perturbation method and homotopy analysis method”, Appl. Math. Comput., 156 (2004), 527–539 | DOI | MR | Zbl

[8] He J. H., “Homotopy perturbation method for bifurcation of nonlinear problems”, Internat. J. Nonlinear Sci. Numer. Simul., 6:2 (2005), 207–208 | Zbl

[9] Rafei M., Ganji D. D., “Explicit solutions of Helmholtz equation and fifth-order KdV equation using homotopy perturbation method”, Internat. J. Nonlinear Sci. Numer. Simul., 7:3 (2006), 321–329

[10] Ganji D. D., Rafei M., “Solitary wave solutions for a generalized Hirota–Satsuma coupled KdV equation by homotopy perturbation method”, Phys. Letts A, 356 (2006), 131–137 | DOI | MR | Zbl

[11] Abbasbandy S., “Homotopy perturbation method for quadratic Riccati differential equation and comparison with Adomian's decomposition method”, Appl. Math. and Comput., 172 (2006), 485–490 | DOI | MR | Zbl

[12] Abbasbandy S., “Numerical solutions of the integral equations: Homotopy perturbation method and Adomian's decomposition method”, Appl. Math. and Comput., 173 (2006), 493–500 | DOI | MR | Zbl

[13] Abbasbandy S., “Application of He's homotopy perturbation method for Laplace transform”, Chaos, Solitons and Fractals, 30 (2006), 1206–1212 | DOI | Zbl

[14] McConnell M., Fokas A. S., Pelloni B., “Localised coherent solutions of the DSI and DSU equations – a numerical study”, Math. and Comput. in Simul., 69 (2005), 424–438 | DOI | MR | Zbl

[15] Davey A., Stewartson K., “On three-dimensional packets of surfaces waves”, Proc. Roy Soc. London. Ser. A, 338 (1974), 101–110 | DOI | MR | Zbl