Exact solutions to the Sharma-Tasso-Olver equation by using improved \(G'/G\)-expansion method. (English) Zbl 1266.35008

Summary: This paper is concerned with a double nonlinear dispersive equation: the Sharma-Tasso-Olver equation. We propose an improved \(G'/G\)-expansion method which is employed to investigate the solitary and periodic traveling waves of this equation. As a result, some new traveling wave solutions involving hyperbolic functions, the trigonometric functions, are obtained. When the parameters are taken as special values, the solitary wave solutions are derived from the hyperbolic function solutions, and the periodic wave solutions are derived from the trigonometric function solutions. The improved \(G'/G\)-expansion method is straightforward, concise and effective and can be applied to other nonlinear evolution equations in mathematical physics.


35C08 Soliton solutions
35C20 Asymptotic expansions of solutions to PDEs
Full Text: DOI


[1] A.-M. Wazwaz, “New solitons and kinks solutions to the Sharma-Tasso-Olver equation,” Applied Mathematics and Computation, vol. 188, no. 2, pp. 1205-1213, 2007. · Zbl 1118.65113
[2] Z. Yan, “Integrability of two types of the (2+1)-dimensional generalized Sharma-Tasso-Olver integro-differential equations,” MM Research, vol. 22, pp. 302-324, 2003.
[3] Z. J. Lian and S. Y. Lou, “Symmetries and exact solutions of the Sharma-Tass-Olver equation,” Nonlinear Analysis: Theory, Methods and Applications, vol. 63, no. 5-7, pp. e1167-e1177, 2005. · Zbl 1224.37038
[4] S. Wang, X.-y. Tang, and S.-Y. Lou, “Soliton fission and fusion: burgers equation and Sharma-Tasso-Olver equation,” Chaos, Solitons & Fractals, vol. 21, no. 1, pp. 231-239, 2004. · Zbl 1046.35093
[5] Y. C. Hon and E. Fan, “Uniformly constructing finite-band solutions for a family of derivative nonlinear Schrödinger equations,” Chaos, Solitons & Fractals, vol. 24, no. 4, pp. 1087-1096, 2005. · Zbl 1068.35156
[6] Y. U\ugurlu and D. Kaya, “Analytic method for solitary solutions of some partial differential equations,” Physics Letters A, vol. 370, no. 3-4, pp. 251-259, 2007. · Zbl 1209.81110
[7] I. E. Inan and D. Kaya, “Exact solutions of some nonlinear partial differential equations,” Physica A, vol. 381, pp. 104-115, 2007.
[8] M. Wang, X. Li, and J. Zhang, “The G\(^{\prime}\)/G-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,” Physics Letters A, vol. 372, no. 4, pp. 417-423, 2008. · Zbl 1217.76023
[9] S. Zhang, J.-L. Tong, and W. Wang, “A generalized G\(^{\prime}\)/G-expansion method for the mKd-V equation with variable coefficients,” Physics Letters A, vol. 372, pp. 2254-2257, 2008. · Zbl 1220.37072
[10] Y.-B. Zhou and C. Li, “Application of modified G\(^{\prime}\)/G-expansion method to traveling wave solutions for Whitham-Broer-Kaup-like equations,” Communications in Theoretical Physics, vol. 51, no. 4, pp. 664-670, 2009. · Zbl 1181.35223
[11] S. Guo and Y. Zhou, “The extended G\(^{\prime}\)/G-expansion method and its applications to the Whitham-Broer-Kaup-like equations and coupled Hirota-Satsuma KdV equations,” Applied Mathematics and Computation, vol. 215, no. 9, pp. 3214-3221, 2010. · Zbl 1187.35209
[12] S. Guo, Y. Zhou, and C. Zhao, “The improved G\(^{\prime}\)/G-expansion method and its applications to the Broer-Kaup equations and approximate long water wave equations,” Applied Mathematics and Computation, vol. 216, no. 7, pp. 1965-1971, 2010. · Zbl 1311.76013
[13] M. Ali Akbar, N. Hj. Mohd. Ali, and E. M. E. Zayed, “A generalized and improved G\(^{\prime}\)/G-expansion method for nonlinear evolution equations,” Mathematical Problems in Engineering, vol. 2012, Article ID 459879, 22 pages, 2012. · Zbl 1264.35078
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