The periodic wave solutions for the (2 + 1)-dimensional dispersive long water equations

Chaos, Solitons and Fractals

Volumn 32, Issue 2, 2007, Pages 847-854

  Sheng, Zhang ^a  

^a BOHAI UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

CHAOS THEORY; DIFFERENTIAL EQUATIONS; FUNCTION EVALUATION; FUNCTIONS;

PERIODIC WAVE SOLUTIONS; SOLITARY WAVES; TRIGONOMETRIC FUNCTIONS; WATER EQUATIONS;

WAVE EQUATIONS;

EID: 33749573230     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2005.11.088     Document Type: Article

References (27)

1. Ablowitz M.J., and Clarkson P.A. Soliton, nonlinear evolution equations and inverse scattering (1991), Cambridge University Press
2. Gardner C.S., Greene J.M., Kruskal M.D., and Miura R.M. Method for solving the Korteweg-de Vries equation. Phys Rev Lett 19 (1967) 1095-1097
3. Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys Rev Lett 27 (1971) 1192
4. Miurs M.R. Bächklund transformation (1978), Springer, Berlin
5. Weiss J., Tabor M., and Carmevale G. The painlevé property for partial differential equations. J Math Phys 24 (1983) 522
6. Zayed E.M.E., Zedan H.A., and Gepreel K.A. Group analysis and modified extended tanh-function to find the invariant solutions and soliton solutions for nonlinear euler equations. Int J Nonlinear Sci Numer Simul 5 3 (2004) 221-234
7. Abdusalam H.A. On an improved complex tanh-function method. Int J Nonlinear Sci Numer Simul 6 2 (2005) 99-106
8. Parkes E.J., and Duffy B.R. Travelling solitary wave solutions to a compound KdV-Burgers equation. Phys Lett A 229 (1997) 217
9. Fan E.G. Extended tanh-function method and it's applications to nonlinear equations. Phys Lett A 277 (2000) 212
10. Yan C. A simple transformation for nonlinear waves. Phys Lett A 224 (1996) 77
11. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int J Nonlinear Sci Numer Simul 6 2 (2005) 207-208
12. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals 3 26 (2005) 695-700
13. El-Shahed M. Application of He's homotopy perturbation method to volterra's integro-differential equation. Int J Nonlinear Sci Numer Simul 6 2 (2005) 163-168
14. Abassy T.A., El-Tawil M.A., and Saleh H.K. The solution of KdV and mKdV equations using adomian pade approximation. Int J Nonlinear Sci Numer Simul 5 4 (2004) 327-340
15. Wang M.L. Exact solution for a compound KdV-Burgers equations. Phys Lett A 213 (1996) 279-287
16. He J.H. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, Solitons & Fractals 4 (2004) 847-851
17. He J.H. Variational approach to (2 + 1)-dimensional dispersive long water equations. Phys Lett A 335 (2005) 182-184
18. Liu H.M. Variational approach to nonlinear electrochemical system. Int J Nonlinear Sci Numer Simul 5 1 (2004) 95-96
19. Liu H.M. Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method. Chaos, Solitons &Fractals 23 (2005) 573-576
20. Hu J.Q. An algebraic method exactly solving two high-dimensional nonlinear evolution equations. Chaos, Solitons & Fractals 23 (2005) 391-398
21. Liu S.K., Fu Z.T., Liu S.D., and Zhao Q. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys Lett A 289 (2001) 69-74
22. Zhou Y.B., Wang M.L., and Wang Y.M. Periodic wave solutions to a coupled KdV equations with variable coefficients. Phys Lett A 308 (2003) 31-36
23. Li X.Y., Yang S., and Wang M.L. The periodic wave solutions for the (3 + 1)-dimensional Klein-Gordon-Schrödinger equations. Chaos, Solitons & Fractals 25 (2005) 629-636
24. Liu J.B., and Yang K.Q. The extended F-expansion method and exact solutions of nonlinear PDEs. Chaos, Solitons & Fractals 22 (2004) 111-121
25. Xia T.C., and Chen D.Y. Dromion and other exact solutions of (2 + 1)-dimensional dispersive long water equations. Chaos, Solitons & Fractals 22 (2004) 577-582
26. Zhang J.F. Multiple soliton-like solutions for (2 + 1)-dimensional dispersive long water equations. Int J Phys 9 (1998) 2449-2455
27. Yan Z.Y., and Zhang H.Q. Study on exact analystical solutions for two systems of nonlinear evolution equations. Acta Phys Sin 8 (2001) 825-833 [in Chinese]