×

Exp-function method for solving the generalized-Zakharov equations. (English) Zbl 1160.35523

Summary: The Exp-function method is used to seek exact solutions of the generalized-Zakharov equations. The validity and reliability of the method is tested by its applications to a class of nonlinear evolution equations of special interest in mathematical physics. As a result, many exact traveling wave solutions are obtained which include single and combined generalized solitonary solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.

MSC:

35Q53 KdV equations (Korteweg-de Vries equations)
35Q51 Soliton equations
35C05 Solutions to PDEs in closed form
35A25 Other special methods applied to PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] He, J. H.; Wu, X. H., Exp-function method for nonlinear wave equations, Chaos, Solitons Fract., 30, 700-708 (2006) · Zbl 1141.35448
[2] He, J. H.; Abdou, M. A., New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos, Solitons Fract., 34, 1421-1429 (2007) · Zbl 1152.35441
[3] Abdou, M. A.; Soliman, A. A.; El-Basyony, S. T., New application of Exp-function method for improved Boussinesq equation, Phys. Lett. A, 369, 469-475 (2007) · Zbl 1209.81091
[4] Zhang, S., Exp-function method for solving Maccari’s system, Phys. Lett. A, 371, 65-71 (2007) · Zbl 1209.65103
[5] Ebaid, A., Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method, Phys. Lett. A, 365, 213-219 (2007) · Zbl 1203.35213
[6] Zhang, S., Application of Exp-function method to a KdV equation with variable coefficients, Phys. Lett. A, 365, 448-453 (2007) · Zbl 1203.35255
[7] Zhang, S., Application of Exp-function method to Riccati equation and new exact solutions with three arbitrary functions of Broer-Kaup-Kupershmidt equations, Phys. Lett. A, 372, 1873-1880 (2008) · Zbl 1220.37071
[8] Yun, Beong In, A non-iterative method for solving non-linear equations, Appl. Math. Comput., 198, 691-699 (2008) · Zbl 1138.65035
[9] Lin, C.; Li, K. M.; Li, Y. Z., Analytical study of the nonlinear dust-acoustic waves in an unmagnetized dusty plasma, Commun. Nonlinear Sci. Numer. Simul., 12, 1190-1194 (2007) · Zbl 1350.82005
[10] Lin, C.; Li, Y. Z.; Li, K. M., The formally variable separation approach for the dust-acoustic solitary waves with dust charge variation, Commun. Nonlinear Sci. Numer. Simul., 12, 920-927 (2007) · Zbl 1111.76341
[11] El-Wakil, S. A.; Abdou, M. A.; Elhanbaly, A., New solitons and periodic wave solutions for nonlinear evolution equations, Phys. Lett. A, 353, 40-47 (2007)
[12] Wang, M. L.; Li, X. Z., Extended F-expansion method and periodic wave solutions for the generalized Zakharov equations, Phys. Lett. A, 343, 48-54 (2005) · Zbl 1181.35255
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.