Exact solutions for the generalized Klein-Gordon equation via a transformation and Exp-function method and comparison with Adomian's method

Journal of Computational and Applied Mathematics

Volumn 223, Issue 1, 2009, Pages 278-290

  Ebaid, A ^a  

^a Ain Shams University   (Egypt)

Author keywords

Exp function method; Generalized Klein Gordon equation; Modified decomposition method

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL TRANSFORMATIONS; NONLINEAR EQUATIONS; OPERATIONS RESEARCH; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DENSITY FUNCTION;

ACCURATE NUMERICAL RESULTS; APPROXIMATE SOLUTIONS; AUXILIARY EQUATION METHODS; EXACT SOLUTIONS; EXP-FUNCTION METHOD; EXP-FUNCTION METHODS; GENERALIZED KLEIN-GORDON EQUATION; GORDON EQUATIONS; JACOBI ELLIPTIC FUNCTIONS; MODIFIED DECOMPOSITION METHOD; MODIFIED DECOMPOSITION METHODS; NEW SOLUTIONS; NONLINEAR PDE; NONLINEAR SCIENCES; NUMERICAL SIMULATIONS; NUMERICAL SOLUTIONS; WIDER RANGES;

LINEAR EQUATIONS;

EID: 54449092407     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2008.01.010     Document Type: Article

References (29)

1. Drazin P.G., and Johnson R.S. Solitons: An Introduction (1983), Cambridge University Press, Cambridge
2. Deeba E.Y., and Khuri S.A. A decomposition method for solving the nonlinear Klein-Gordon equation. Journal of Computational Physics 124 (1996) 442-448
3. Liu S., Fu Z., Liu S., and Zhao Q. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Physics Letters A 289 (2001) 69-74
4. Sirendaoreji. Auxiliary equation method and new solutions of Klein-Gordon equations. Chaos, Solitons & Fractals 31 4 (2007) 943-950
5. Zhang H. Extended Jacobi elliptic function expansion method and its applications. Communications in Nonlinear Science and Numerical Simulation 12 5 (2007) 627-635
6. Wazwaz A.M. A reliable modification of Adomian's decomposition method. Applied Mathematics and Computation 102 (1999) 77-96
7. Wazwaz A.M. The modified decomposition method applied to unsteady flow of gas through a porous medium. Applied Mathematics and Computation 118 (2001) 123-132
8. Parkes E.J., and Duffy B.R. An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations. Computer Physics Communications 98 (1996) 288-300
9. Li D.S., Gao F., and Zhang H.Q. Solving the (2+1)-dimensional higher order Broer-Kaup system via a transformation and tanh-function method. Chaos, Solitons & Fractals 20 5 (2004) 1021-1025
10. Bai C.L., and Zhao H. Generalized extended tanh-function method and its application. Chaos, Solitons & Fractals 27 4 (2006) 1026-1035
11. Abdusalam H.A. On an improved complex tanh-function method. International Journal of Nonlinear Sciences and Numerical Simulation 6 2 (2005) 99-106
12. Fu Z., Liu S., Liu S., and Zhaoa Q. New Jacobi elliptic function expansion and new periodic solutions of nonlinear wave equations. Physics Letters A 290 (2001) 72-76
13. Liu G.-T., and Fana T.-Y. New applications of developed Jacobi elliptic function expansion methods. Physics Letters A 345 (2005) 161-166
14. Liu Q., and Zhu J.-M. Exact Jacobian elliptic function solutions and hyperbolic function solutions for Sawada-Kotere equation with variable coefficient. Physics Letters A 352 (2006) 233-238
15. Fan E. Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics. Chaos, Solitons & Fractals 16 (2003) 819-839
16. Zhang J.-L., Wang M.-L., Wang Y.-M., and Fang Z.-D. The improved F-expansion method and its applications. Physics Letters A 350 (2006) 103-109
17. Liu J., and Yang K. The extended F-expansion method and exact solutions of nonlinear PDEs. Chaos, Solitons & Fractals 22 (2004) 111-121
18. Zhang H. New exact travelling wave solutions for some nonlinear evolution equations. Chaos, Solitons & Fractals 26 (2005) 921-925
19. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer. Acad., Boston
20. Wazwaz AM. Construction of solitary wave solutions and rational solutions for the KdV equation by Adomian decomposition method. Chaos, Solitons & Fractals 12 (2001) 2283-2293
21. Wazwaz AM. A study of nonlinear dispersive equations with solitary-wave solutions having compact support. Mathematics and Computers in Simulation 56 (2001) 269-276
22. Kaya D., and El-Sayed S.M. A numerical solution of the Klein-Gordon equation and convergence of the decomposition method. Appl. Math. Computational 156 (2004) 341-353
23. Cherruault Y., Inc M., and Abbaoui K. On the solution of the non-linear Korteweg-de Vries equation by the decomposition method. Kybernetes 31 5 (2002) 766-772
24. He J.-H., and Wu X.-H. Exp-function method for nonlinear wave equations. Chaos, Solitons & Fractals 30 3 (2006) 700-708
25. He J.-H., and Abdou M.A. New periodic solutions for nonlinear evolution equations using Exp-function method. Chaos, Solitons & Fractals 34 5 (2007) 1421-1429
26. Cherruault Y. Convergence of Adomian's method. Kybernetes 9 (1988) 31-38
27. Cherruault Y., and Adomian G. Decomposition Method; A new proof of Convergence. Mathematical and Computer Modelling 18 (1993) 103-106
28. Cherruault Y., Adomian G., Abbaoui K., and Rach R. Further remarks on Convergence of decomposition. International Journal of Bio-Medical Computing 38 (1995) 89-93
29. Abassy T.A., El-Tawil M.A., and Saleh H.K. The solution of Burgers' and good Boussinesq equations using ADM-Padè technique. Chaos, Solitons & Fractals 32 3 (2007) 1008-1026