Article Sidebar

Submitted
Apr 28, 2017
Published
Dec 1, 2015
Download
PDF
Statistic
Read Counter : 317 Download : 220

Main Article Content

Abstract

In this paper, we employ mapping methods to construct exact travelling wave solutions for a modified Korteweg-de Vries equation. We have derived periodic wave solutions in terms of Jacobi elliptic functions, kink solutions and singular wave solutions in terms of hyperbolic functions.  

Keywords

Jacobi elliptic functions Korteweg-de Vries equation Solitary wave solutions Travelling wave solutions.

Article Details

References

  1. Malfliet, W. The tanh method: 1. Exact solutions of nonlinear evolution and wave equations. Physica Scripta, 1996, 54, 563-568.
  2. He, J.H. and Wu, X.H. Exp-function method for nonlinear wave equations. Chaos Solitons and Fractals, 2006, 30, 700- 708.
  3. Liu, J., Yang, L. and Yang, K., Jacobi elliptic function solutions of some nonlinear PDEs. Physics Letters A, 2004, 325, 268-275.
  4. Peng, Y. Exact periodic wave solutions to a new Hamiltonian amplitude equation. Journal of the Physical Society of Japan, 2003, 72, 1356-1359.
  5. Krishnan, E.V. and Peng, Y. A new solitary wave solution for the new Hamiltonian amplitude equation. Journal of the Physical Society of Japan, 2005, 74, 896-897.
  6. Krishnan, E.V. and Biswas, A., Solutions to the Zakharov-Kuznetsov equation with higher order nonlinearity by mapping and ansatz methods. Physics of Wave Phenomena, 2010, 18, 256-261.
  7. Alzaidy, J.F. Extended mapping method and its applications to nonlinear evolution equations. Journal of Applied Mathematics, 2012, Article ID 597983, 14 pages.
  8. Hirota, R. and Satsuma, J. Soliton solutions of a coupled Korteweg-de Vries equation. Physics Letters A, 1981, 85, 407-408 .
  9. Dodd, R. and Fordy, A.P. On the integrability of a system of coupled KdV equations. Physics Letters A, 1982, 89, 168-170 .
  10. Krishnan, E.V. Remarks on a system of coupled nonlinear wave equations. Journal of Mathematical Physics, 1990, 31, 1155-1156.
  11. Wang, M.L., Solitary wave solutions for variant Boussinesq equations. Physics Letters A, 1995, 199, 169-172
  12. Lawden, D.F., Elliptic Functions and Applications, Springer Verlag, 1989.
  13. Peng, Y.Z. and Krishnan, E.V. Exact travelling wave solutions to the (3+1)-dimensional Kadomtsev-Petviashvili equation. Acta Physica Polonica, 2005, 108, 421-428.
  14. Gurses, M. and Peckcan, A. 2+1 KdV(N) equations. Journal of Mathematical Physics, 2011, 52, 1-14.
  15. Wazwaz, A.M. A modified KdV-type equation that admits a variety of travelling wave solutions: kinks, solitons. peakons and cuspons, Physica Scripta, 2012, 86, 1-6.
  16. Ebadi, G., Krishnan, E.V., Labidi, M. Zerrard, E. and Biswas, A. Analytical and numerical solutions to the Davey-Stewartson equation with power law nonlinearity. Waves in Random and Complex Media, 2011, 21, 559-590.