Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method. (English) Zbl 1160.35517
Summary: He’s homotopy perturbation method (HPM), which does not need small parameter in the equation is implemented for solving the nonlinear Hirota-Satsuma coupled KdV partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of Adomian’s decomposition method has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
homotopy perturbation method; Helmholtz equation; FKdV equation; nonlinear partial differential equationsReferences:
| [1] | Wu, Y. T.; Geng, X. G.; Hu, X. B.; Zhu, S. M., Phys. Lett. A, 255, 259 (1999) · Zbl 0935.37029 |
| [2] | Hirota, R.; Satsuma, J., Phys. Lett. A, 85, 407 (1981) |
| [3] | Fan, E., Phys. Lett. A, 282, 18 (2001) · Zbl 0984.37092 |
| [4] | Malfliet, W., Am. J. Phys., 60, 650 (1992) · Zbl 1219.35246 |
| [5] | Parkes, E. J.; Duffy, B. R., Comput. Phys. Commun., 98, 288 (1996) · Zbl 0948.76595 |
| [6] | Yu, Y.; Wang, Q.; Zhang, H., Chaos Solitons Fractals, 26, 5, 1415 (2005) · Zbl 1106.35087 |
| [7] | Yong, X. L.; Zhang, H. Q., Chaos Solitons Fractals, 26, 4, 1105 (2005) · Zbl 1072.35584 |
| [8] | Zayed, E. M.E.; Zedan, H. A.; Gepreel, K. A., Chaos Solitons Fractals, 22, 2, 285 (2004) · Zbl 1069.35080 |
| [9] | He, J. H.; Wu, X. H., Chaos Solitons Fractals, 29, 1, 108 (2006) · Zbl 1147.35338 |
| [10] | Kaya, D., Appl. Math. Comput., 147, 69 (2004) · Zbl 1037.35069 |
| [11] | He, J. H., Appl. Math. Comput., 151, 287 (2004) |
| [12] | He, J. H., Appl. Math. Comput., 156, 527 (2004) · Zbl 1062.65074 |
| [13] | He, J. H., Appl. Math. Comput., 156, 3, 591 (2004) · Zbl 1061.65040 |
| [14] | He, J. H., Int. J. Nonlinear Sci. Numer. Simul., 6, 2, 207 (2005) · Zbl 1401.65085 |
| [15] | He, J. H., Chaos Solitons Fractals, 26, 695 (2005) · Zbl 1072.35502 |
| [16] | He, J. H., Chaos Solitons Fractals, 26, 3, 827 (2005) · Zbl 1093.34520 |
| [17] | He, J. H., Phys. Lett. A, 350, 87 (2006) |
| [18] | Ganji, D. D.; Rajabi, A., Int. Commun. Heat Mass Transfer, 33, 3, 391 (2006) |
| [19] | He, J. H., J. Comput. Math. Appl. Mech. Eng., 178, 257 (1999) · Zbl 0956.70017 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
