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Application of Improved (G′/G)–Expansion Method to Traveling Wave Solutions of Two Nonlinear Evolution Equations

Published online by Cambridge University Press:  03 June 2015

Xiaohua Liu ,
Weiguo Zhang  and
Zhengming Li
Xiaohua Liu*
Affiliation:
Department of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Weiguo Zhang*
Affiliation:
Department of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Zhengming Li*
Affiliation:
Department of Business, University of Shanghai for Science and Technology, Shanghai, 200093 China
*
Email: [email protected]
Corresponding author. Email: [email protected]
Email: [email protected]
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Abstract

In this work, the improved (G′/G)-expansion method is proposed for constructing more general exact solutions of nonlinear evolution equation with the aid of symbolic computation. In order to illustrate the validity of the method we choose the RLW equation and SRLW equation. As a result, many new and more general exact solutions have been obtained for the equations. We will compare our solutions with those gained by the other authors.

Keywords

35C0735C0835A25RLW equationSRLW equationimproved (G′/G)-expansion methodtraveling wave solution
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 4 , Issue 1 , February 2012 , pp. 122 - 130
Copyright
Copyright © Global-Science Press 2012

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References

[1] Ablowitz, M. J. and Clarkson, P. A., Solitons, Nonlinear Evolution and Inverse Scattering, Cambrige University Press, 1991.CrossRefGoogle Scholar
[2] Hirota, R., Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett., 27 (1971), pp. 1192–1194.Google Scholar
[3] He, J. H., Variational iteration method-some recent results and new interpretations, J. Comput. Appl. Math., 207 (2007), pp. 3–17.CrossRefGoogle Scholar
[4] Wang, M. L., Zhou, Y. B. and Li, Z. B., Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Phys. Lett. A., 216 (1996), pp. 67–75.CrossRefGoogle Scholar
[5] Lamb, G. L., Bucklund transformations for certain nonlinear evolution equations, J. Math. Phys., 15 (1974), pp. 2157–2165.CrossRefGoogle Scholar
[6] Wazawaz, A.M., New traveling wave solutions of differential physical structures to generalized BBM equation, Phys. Lett. A., 355 (2006), pp. 358–362.CrossRefGoogle Scholar
[7] Kuznetsov, E. A., On the Ito-type coupled nonlinear wave equation, J. Phys. Soc. Jpn., 55 (1986), pp. 3753–3755.Google Scholar
[8] Zhang, S., A generalized new auxiliary equation method and its application to the (2+1)-dimensional breaking soliton equations, Appl. Math. Comput., 190 (2007), pp. 510–516.Google Scholar
[9] Yomba, E., A generalized auxiliary equation method and its application to nonlinear Klein-Gordon and generalized nonlinear Camassa-Holm equations, Phys. Lett. A., 372 (2008), pp. 1048–1060.CrossRefGoogle Scholar
[10] Kangalgil, F. and Ayaz, F., New exact traveling wave solutions for the Ostrovsky equation, Pyys. Lett. A., 372 (2008), pp. 1831–1835.CrossRefGoogle Scholar
[11] Wang, M., Li, X. and Zhang, J., The (G’/G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A., 372 (2008), pp. 417–423.CrossRefGoogle Scholar
[12] Kabir, M. M., Borhanifar, A. and Abazari, R., Application of (G’/G)-expansion method to Regularized Long Wave (RLW) equation, Comput. Math. Appl., 61 (2011), pp. 2044–2047.CrossRefGoogle Scholar
[13] Xu, F., Application of Exp-function method to Symmetric Regularized Long Wave (SRLW) equation, Phys. Lett. A., 372 (2008), pp. 252–257.CrossRefGoogle Scholar
[14] Zhang, S., Wang, W. and Tong, J. L., A generalized (G′’/G)-expansion method and its application to the (2+1)-dimensional Broer-Kaup equations, Appl. Math. Comput., 209 (2009), pp. 399–404.Google Scholar
[15] Shehata, A. R., The traveling wave solutions of the perturbed nonlinear Schroinger equation and the cubic-quintic Ginzburg Landau equation using the modified (G’/G) expansion method, Appl. Math. Comput., 217 (2010), pp. 1–10.Google Scholar
[16] Lv, H. L., Liu, X. Q. and Niu, L., A generalized (G′’/G)-expansion method and its applications to nonlinear evolution equations, Appl. Math. Comput., 215 (2010), pp. 3811–3816.Google Scholar
[17] Zhang, H., New application of the (G′’ /G)-expansion method, Commun. Nonlinear. Sci. Numer. Sim., 14 (2009), pp. 3220–3225.CrossRefGoogle Scholar
[18] Ma, W. X. and Fuchssteiner, B., Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation, Int. J. Nonlinear. Mech., 31 (1996), pp. 329–338.CrossRefGoogle Scholar
[19] Ma, W. X. and Lee, Jyh Hao, A transformed rational function method and exact solutions to the (3+1) dimensional Jimbo-Miwa equation, Chaos. Solitons. Frac, 42 (2009), pp. 1356–1363.CrossRefGoogle Scholar
[20] Ma, W. X. and Fan, E.G., Linear superposition principle applying to Hirota bilinear equations, Comput. Math. Appl., 61 (2011), pp. 950–959.CrossRefGoogle Scholar
[21] Ma, W. X., Huang, T. W. and Zhang, Y., A multiple exp-function method for nonlinear differential equations and its application, Phys. Scrip., 82 (2010), 065003.CrossRefGoogle Scholar
[22] Peregrine, D. H., Calculations of the development of an undular bore, J. Fluid. Mech., 25 (1966), pp. 321–330.CrossRefGoogle Scholar
[23] Benjamin, T. B., Bona, J. L. and Mahony, J., Model equations for waves in nonlinear dispersive systems, J. Philos. Trans. Roy. Soc. Lond., 227 (1972), pp. 47–78.Google Scholar