NEW TRAVELING WAVE SOLUTIONS TO THE SEVENTH-ORDER SAWADA-KOTERA EQUATION

  • Feng, Jishe (Department of Mathematics, Longdong University)
  • Received : 2010.03.05
  • Accepted : 2010.04.17
  • Published : 2010.09.30

Abstract

We use the (G'/G)-expansion method to seek the traveling wave solution of the Seventh-order Sawada-Kotera Equation. The solutions that we get are more general than the solutions given in literature. It is shown that the (G'/G)-expansion method provides a very effective and powerful mathematical tool for solving nonlinear equations in mathematical physics.

Keywords

References

  1. Salah M. El-Sayed and Dogan Kaya, An application of the ADM to seven-order Sawadakotara equations, Appl. Math. Comput.157 (2004), 93-101. https://doi.org/10.1016/j.amc.2003.08.104
  2. M.L. Wang, X. Z. Li and J. L. Zhang, The (G'/G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A, 372 (2008), 417-423. https://doi.org/10.1016/j.physleta.2007.07.051
  3. A. Bekir, Application of the (G'/G)-expansion method for nonlinear evolution equations, Phys. Lett. A, 372 (2008), 3400-3406. https://doi.org/10.1016/j.physleta.2008.01.057
  4. J. Zhang, X. Wei and Y. Lu, A generalized (G'/G)-expansion method and its applications, Phys. Lett. A, 372 (2008), 3653-3658. https://doi.org/10.1016/j.physleta.2008.02.027
  5. S. Zhang, J.L. Tong and W. Wang, A generalized (G'/G)-expansion method for the mKdV equation with variable coefficients, Phys. Lett. A, 372 (2008). 2254-2257. https://doi.org/10.1016/j.physleta.2007.11.026
  6. S. Zhang, L. Dong, J.M. Ba and Y.N. Sun, The (G'/G)-expansion method for nonlinear differential-difference equations, Phys. Lett. A, 373 (2009), 905-910. https://doi.org/10.1016/j.physleta.2009.01.018
  7. H. Q. Zhang, New application of the (G'/G)-expansion method, Commun. Nonlinear Sci. Numer. Simulat. 14(2009), 3220-3225. https://doi.org/10.1016/j.cnsns.2009.01.006
  8. I.Aslan and T.Ozis,, Analytic study on two nonlinear evolution equations by using the (G'/G)-expansion method, Appl. Math. Comput. 209(2009), 425-429. https://doi.org/10.1016/j.amc.2008.12.064
  9. I.Aslan and T.Ozis, On the validity and reliability of the (G'/G)-expansion method by using higher-order nonlinear equations, Appl. Math. Comput. doi:10.1016/j.amc.2009.01.075150.
  10. I.Aslan, Exact and explicit solutions to some nonlinear evolution equations by utilizing the (G'/G)-expansion method, Appl. Math. Comput. doi:10.1016/j.amc.2009.05.038.
  11. T. Ozis and I. Aslan, Symbolic Computation and Construction of New Exact Travelling Wave Solutions to Fitzhugh-Nagumo and Klein-Gordon Equations, Z. Naturforsch, 64a(2009), 15-20.
  12. T. Ozis and I. Aslan, Symbolic computations and exact and explicit solutions of some nonlinear evolution equations in mathematical physics, Commun. Theor. Phys. 51(2009), 577-580. https://doi.org/10.1088/0253-6102/51/4/01
  13. H. Gao and R-X. Zhao, New application of the (G'/G)-expansion method to higher-order nonlinear equations, Appl. Math. Comput. doi:10.1016/j.amc.2009.08.041.
  14. E. M. E. Zayed, New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized (G'/G)-expansion method, J. Phys. A: Math. Theor. 42 (2009), 195202-195215. https://doi.org/10.1088/1751-8113/42/19/195202
  15. E. M. E. Zayed, The (G'/G)-expansion method and its applications to some nonlinear evolution equations in the mathematical physics,, J. Appl.Math. and Computing 30(2009), 89-103. https://doi.org/10.1007/s12190-008-0159-8
  16. Zhou Y. Bin and L. Chao, Application of modified (G'/G)-expansion method to traveling wave solutions for Whitham-Broer-Kaup-Like equations, Commu. Theore. Phys. 51(2009), 664-670. https://doi.org/10.1088/0253-6102/51/4/17
  17. E. M. E. Zayed and Khaled A. Gepreel, Some applications of the (G'/G)-expansion method to non-linear partial differential equations, Appl. Math. Comput.212(2009), 1-13. https://doi.org/10.1016/j.amc.2009.02.009
  18. E. M. E. Zayed and K. A. Gepreel, The (G'/G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics, J. Math. Phys. 50 (2009), 013502-013513. https://doi.org/10.1063/1.3033750
  19. E. M. E. Zayed and S. Al-Joudi, Applications of an Improved (G'/G)-expansion Method to Nonlinear PDEs in Mathematical Physics, AIP Conf. Proc. Amer. Institute of Physics. 1168(2009), 371-376.
  20. E.J. Parkes and B.R, Duffy, An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations, Comput. Phys. Commun. 98(1996), 288-300. https://doi.org/10.1016/0010-4655(96)00104-X