Solving the fifth order Caudrey-Dodd-Gibbon (CDG) equation using the exp-function method

Applied Mathematics and Computation

Volumn 206, Issue 1, 2008, Pages 70-73

  Xu, Yu Guang ^a   Zhou, Xin Wei ^a   Yao, Li ^a  

^a KUNMING UNIVERSITY   (China)

Author keywords

Caudrey Dodd Gibbon (CDG) equation; Exp function method

Indexed keywords

CAUDREY-DODD-GIBBON (CDG) EQUATION; EXP-FUNCTION METHOD; EXP-FUNCTION METHODS; SOLITARY SOLUTIONS;

PROBABILITY DENSITY FUNCTION;

EID: 55949130212     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2008.08.052     Document Type: Article

References (32)

1. Aiyer R.N., Fuchssteiner B., and Oevel W. Solitons and discrete eigenfunctions of the recursion operator of non-linear evolution equations: the Caudrey-Dodd-Gibbon-Sawada-Kotera equations. J. Phys. A: Math. General 19 (1986) 3755-3770
2. Wazwaz A.M. Analytic study of the fifth order integrable nonlinear evolution equations by using the tanh method. Appl. Math. Comput. 174 (2006) 289-299
3. Wazwaz A.M. Multiple-soliton solutions for the fifth order Caudrey-Dodd-Gibbon (CDG) equation. Appl. Math. Comput. 197 (2008) 719-724
4. Cao C.W., Wu Y.T., and Geng X.G. On quasi-periodic solutions of the 2 + 1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation. Phys. Lett. A 256 (1999) 59-65
5. Lou S.Y. Twelve sets of symmetries of the Caudrey-Dodd-Gibbon-Sawada-Kotera equation. Phys. Lett. A 175 (1993) 23-26
6. He J.H. New interpretation of homotopy perturbation method. Int. J. Mod. Phys. B 20 (2006) 2561-2568
7. Tari H., Ganji D.D., and Rostamian M. Approximate solutions of K (2,2), KdV and modified KdV equations by variational iteration method, homotopy perturbation method and homotopy analysis method. Int. J. Nonlin. Sci. Num. 8 (2007) 203-210
8. Ozis T., and Yildirim A. Traveling wave solution of Korteweg-de Vries equation using He's homotopy perturbation method. Int. J. Nonlin. Sci. Num. 8 (2007) 239-242
9. Sadighi A., and Ganji D.D. Solution of the generalized nonlinear Boussinesq equation using homotopy perturbation and variational iteration methods. Int. J. Nonlin. Sci. Num. 8 (2007) 435-443
10. Wazwaz A.M. A study on linear and nonlinear Schrodinger equations by the variational iteration method. Chaos Solitons Fractals 37 (2008) 1136-1142
11. Wazwaz A.M. The variational iteration method for a reliable treatment of the linear and the nonlinear Goursat problem. Appl. Math. Comput. 193 (2007) 455-462
12. Wazwaz A.M. The variational iteration method for solving linear and nonlinear systems of PDEs. Comput. Math. Appl. 54 (2007) 895-902
13. Wazwaz A.M. The variational iteration method: A reliable analytic tool for solving linear and nonlinear wave equations. Comput. Math. Appl. 54 (2007) 926-932
14. He J.H., and Wu X.H. Variational iteration method: New development and applications. Comput. Math. Appl. 54 (2007) 881-894
15. He J.H. Variational iteration method - Some recent results and new interpretations. J. Comput. Appl. Math. 207 (2007) 3-17
16. He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos Solitons Fractals 29 (2006) 108-113
17. Odibat Z.M., and Momani S. Application of variational iteration method to Nonlinear differential equations of fractional order. Int. J. Nonlin. Sci. Num. 7 (2006) 27-36
18. Tao Z.L. Variational approach to the inviscid compressible fluid. Acta Appl. Math. 100 (2008) 291-294
19. He J.H. Some asymptotic methods for strongly nonlinear equations. Int. J. Mod. Phys. B 20 (2006) 1141-1199
20. He J.H., and Wu X.H. Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30 (2006) 700-708
21. Benn Wu X.H., and He J.H. Solitary solutions, periodic solutions and compacton-like solutions using the exp-function method. Comput. Math. Appl. 54 (2007) 966-986
22. He J.H., and Zhang L.N. Generalized solitary solution and compacton-like solution of the Jaulent-Miodek equations using the exp-function method. Phys. Lett. A 372 (2008) 1044-1047
23. He J.H., and Abdou M.A. New periodic solutions for nonlinear evolution equations using exp-function method. Chaos Solitons Fractals 34 (2007) 1421-1429
24. (Benn) Wu X.H., and He J.H. Exp-function method and its application to nonlinear equations. Chaos Solitons Fractals 38 (2008) 903-910
25. He J.H. Non-perturbative Methods for Strongly Nonlinear Problems (2006), de-Verlag im Internet GmbH, Berlin
26. Bekir A., and Boz A. Exact solutions for a class of nonlinear partial differential equations using exp-function method. Int. J. Nonlin. Sci. Num. 8 (2007) 505-512
27. Zhou X.W. Exp-function method for solving Huxley Equation. Math. Prob. Eng. 2008 (2008) Article ID 538489
28. Zhou X.W. Exp-function method for solving Fisher's Equation. J. Phys.: Confer. Series 96 (2008) 012063
29. Zhou X.W., Wen Y.X., and He J.H. Exp-function method to solve the nonlinear dispersive K(m,n) equations. Int. J. Nonlin. Sci. Num. 9 (2008) 301-306
30. Zhu S.D. Exp-function method for the Hybrid-Lattice system. Int. J. Nonlin. Sci. Num. 8 (2007) 461-464
31. Zhu S.D. Exp-function method for the discrete mKdV lattice. Int. J. Nonlin. Sci. Num. 8 (2007) 465-468
32. He J.H. An elementary introduction to recently developed asymptotic methods and nanomechanics in textile engineering. Int. J. Mod. Phys. B 22 (2008) 3487-3578