A generalized F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equations

Applied Mathematics and Computation

Volumn 183, Issue 2, 2006, Pages 1190-1200

  Zhang, Sheng ^a   Xia, TieCheng ^a,b  

^a BOHAI UNIVERSITY   (China)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

Generalized F expansion method; Jacobi elliptic function solutions; Soliton like solutions; Trigonometric function solutions

Indexed keywords

FUNCTION EVALUATION; SOLITONS;

GENERALIZED F-EXPANSION METHOD; JACOBI ELLIPTIC FUNCTION SOLUTIONS; SOLITON-LIKE SOLUTIONS; TRIGONOMETRIC FUNCTION SOLUTIONS;

PARTIAL DIFFERENTIAL EQUATIONS;

EID: 33845792126     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2006.06.043     Document Type: Article

References (36)

1. Ablowitz M.J., and Clarkson P.A. Soliton, Nonlinear Evolution Equations and Inverse Scattering (1991), Cambridge University Press, New York
2. Hirota R. Exact solution of the Korteweg-de Vries equation for multiple collisions of solitons. Phys. Rev. Lett. 27 (1971) 1192-1194
3. Miurs M.R. Backlund Transformation (1978), Springer, Berlin
4. Weiss J., Tabor M., and Carnevale G. The painlevé property for partial differential equations. J. Math. Phys. 24 (1983) 522-526
5. Yan C. A simple transformation for nonlinear waves. Phys. Lett. A 224 (1996) 77-84
6. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. Int. J. Nonlinear Sci. Numer. Simul. 6 (2005) 207-208
7. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons & Fractals 26 (2005) 695-700
8. El-Shahed M. Application of He's homotopy perturbation method to Volterra's integro-differential equation. Int. J. Nonlinear Sci. Numer. Simul. 6 (2005) 163-168
9. 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 (2004) 327-340
10. Wang M.L. Exact solution for a compound KdV-Burgers equations. Phys. Lett. A 213 (1996) 279
11. He J.H. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, Solitons & Fractals 19 (2004) 847-851
12. He J.H. Variational approach to (2 + 1)-dimensional dispersive long water equations. Phys. Lett. A 335 (2005) 182-184
13. Liu H.M. Variational approach to nonlinear electrochemical system. Int. J. Nonlinear Sci. Numer. Simul. 5 (2004) 95-96
14. Liu H.M. Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method. Chaos, Solitons & Fractals 23 (2005) 573-576
15. Hu J.Q. An algebraic method exactly solving two high-dimensional nonlinear evolution equations. Chaos, Solitons & Fractals 23 (2005) 391-398
16. Malfliet W. Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60 (1992) 650-654
17. Parkes E.J., and Duffy B.R. Travelling solitary wave solutions to a compound KdV-Burgers equation. Phys. Lett. A 229 (1997) 217-220
18. Fan E.G. Extended tanh-function method and its applications to nonlinear equations. Phys. Lett. A 277 (2000) 212-218
19. Yan Z.Y., and Zhang H.Q. New explicit solitary wave solutions and periodic wave solutions for Whitham-Broer-Kaup equation in shallow water. Phys. Lett. A 285 (2001) 355-362
20. 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 (2004) 221-234
21. Abdusalam H.A. On an improved complex tanh-function method. Int. J. Nonlinear Sci. Numer. Simul. 6 (2005) 99-106
22. Xie F.D., Zhang Y., and Lü Z.S. Symbolic computation in non-linear evolution equation: application to (3 + 1)-dimensional Kadomtsev-Petviashvili equation. Chaos, Solitons & Fractals 24 (2005) 257-263
23. 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
24. Wang M.L., and Zhou Y.B. The periodic wave solutions for the Klein-Gordon-Schrödinger equations. Phys. Lett. A 318 (2003) 84-92
25. Wang M.L., Wang Y.M., and Zhang J.L. The periodic wave solutions for two systems of nonlinear wave equations. Chin. Phys. 12 (2003) 1341-1348
26. Zhou Y.B., Wang M.L., and Miao T.D. The periodic wave solutions and solitary wave solutions for a class of nonlinear partial differential equations. Phys. Lett. A 323 (2004) 77-88
27. 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
28. Fu Z.T., Liu S.K., Liu S.D., and Zhao Q. New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Phys. Lett. A 290 (2001) 72-76
29. Parkes E.J., Duffy B.R., and Abbott P.C. The Jacobi elliptic-function method for finding periodic-wave solutions to nonlinear evolution equations. Phys. Lett. A 295 (2002) 280-286
30. Liu J., Yang L., and Yang K. Nonlinear transform and Jacobi elliptic function solutions of nonlinear equations. Chaos, Solitons & Fractals 20 (2004) 1157-1164
31. 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
32. Wang M.L., and Li X.Z. Applications of F-expansion to periodic wave solutions for a new Hamiltonian amplitude equation. Chaos, Solitons & Fractals 24 (2005) 1257-1268
33. Liu J., and Yang K.Q. The extended F-expansion method and exact solutions of nonlinear PDEs. Chaos, Solitons & Fractals 22 (2004) 111-121
34. Wang D.S., and Zhang H.Q. Further improved F-expansion method and new exact solutions of Konopelchenko-Dubrovsky equation. Chaos, Solitons & Fractals 25 (2005) 601-610
35. Chen J., He H.S., and Yang K.Q. A generalized F-expansion method and its application in high-dimensional nonlinear evolution equation. Commun. Theor. Phys. (Beijing, China) 44 (2005) 307-310
36. Xia T.C., Lü Z.S., and Zhang H.Q. Symbolic computation and new families of exact soliton-like solutions of Konopelchenko-Dubrovsky equations. Chaos, Solitons & Fractals 20 (2004) 561-566