Skip to main content Accessibility help

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

  • Xiaohua Liu (a1), Weiguo Zhang (a1) and Zhengming Li (a2)


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.


Corresponding author

Corresponding author. Email:


Hide All
[1] Ablowitz, M. J. and Clarkson, P. A., Solitons, Nonlinear Evolution and Inverse Scattering, Cambrige University Press, 1991.
[2] Hirota, R., Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons, Phys. Rev. Lett., 27 (1971), pp. 11921194.
[3] He, J. H., Variational iteration method-some recent results and new interpretations, J. Comput. Appl. Math., 207 (2007), pp. 317.
[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. 6775.
[5] Lamb, G. L., Bucklund transformations for certain nonlinear evolution equations, J. Math. Phys., 15 (1974), pp. 21572165.
[6] Wazawaz, A.M., New traveling wave solutions of differential physical structures to generalized BBM equation, Phys. Lett. A., 355 (2006), pp. 358362.
[7] Kuznetsov, E. A., On the Ito-type coupled nonlinear wave equation, J. Phys. Soc. Jpn., 55 (1986), pp. 37533755.
[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. 510516.
[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. 10481060.
[10] Kangalgil, F. and Ayaz, F., New exact traveling wave solutions for the Ostrovsky equation, Pyys. Lett. A., 372 (2008), pp. 18311835.
[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. 417423.
[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. 20442047.
[13] Xu, F., Application of Exp-function method to Symmetric Regularized Long Wave (SRLW) equation, Phys. Lett. A., 372 (2008), pp. 252257.
[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. 399404.
[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. 110.
[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. 38113816.
[17] Zhang, H., New application of the (G′’ /G)-expansion method, Commun. Nonlinear. Sci. Numer. Sim., 14 (2009), pp. 32203225.
[18] Ma, W. X. and Fuchssteiner, B., Explicit and exact solutions to a Kolmogorov-Petrovskii-Piskunov equation, Int. J. Nonlinear. Mech., 31 (1996), pp. 329338.
[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. 13561363.
[20] Ma, W. X. and Fan, E.G., Linear superposition principle applying to Hirota bilinear equations, Comput. Math. Appl., 61 (2011), pp. 950959.
[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.
[22] Peregrine, D. H., Calculations of the development of an undular bore, J. Fluid. Mech., 25 (1966), pp. 321330.
[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. 4778.



Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed