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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.

35Q53KdV-like (Korteweg-de Vries) equations
35Q51Soliton-like equations
35C05Solutions of PDE in closed form
35A25Other special methods (PDE)
Full Text: DOI
[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
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[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 05161260
[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
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