Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method

Computers and Mathematics with Applications

Volumn 54, Issue 7-8, 2007, Pages 966-986

 

^a Benn)   (China)

Author keywords

Exp function method; Periodic solutions and compacton like solutions; Solitary solutions

Indexed keywords

NONLINEAR EQUATIONS; SOLITONS; TIME VARYING SYSTEMS;

EXP-FUNCTION METHOD; SOLITARY SOLUTIONS;

FUNCTIONAL ANALYSIS;

EID: 34748862326     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.12.041     Document Type: Article

References (36)

1. He J.H., and Wu X.H. Construction of solitary solution and compacton-like solution by variational iteration method. Chaos, Solitons and Fractals 29 (2006) 108-113
2. Odibat Z.M., and Momani S. Application of variational iteration method to nonlinear differential equations of fractional order. International Journal of Nonlinear Science and Numerical Simulation 7 (2006) 27-34
3. Bildik N., and Konuralp A. The use of variational iteration method, differential transform method and adomian decomposition method for solving different types of nonlinear partial differential equations. International Journal of Nonlinear Science and Numerical Simulation 7 (2006) 65-70
4. Momani S., and Abuasad S. Application of He's variational iteration method to Helmholtz equation. Chaos, Solitons and Fractals 27 (2006) 1119-1123
5. He J.H. Application of homotopy perturbation method to nonlinear wave equations. Chaos, Solitons and Fractals 26 (2005) 695-700
6. He J.H. Homotopy perturbation method for bifurcation of nonlinear problems. International Journal of Nonlinear Science and Numerical Simulation 6 (2005) 207-208
7. He J.H. New interpretation of homotopy perturbation method. International Journal of Modern Physics B 20 18 (2006) 2561-2568
8. El-Shahed M. Application of He's homotopy perturbation method to Volterra's integro-differential equation. International Journal of Nonlinear Science and Numerical Simulation 6 (2005) 163-168
9. Siddiqui A.M., Mahmood R., and Ghori Q.K. Thin film flow of a third grade fluid on a moving belt by He's homotopy perturbation method. International Journal of Nonlinear Science and Numerical Simulation 7 (2006) 7-14
10. Cai X.C., Wu W.Y., and Li M.S. Approximate period solution for a kind of nonlinear oscillator by He's perturbation method. International Journal of Nonlinear Science and Numerical Simulation 7 (2006) 109-112
11. He J.H. Variational principles for some nonlinear partial differential equations with variable coefficients. Chaos, Solitons and Fractals 19 (2004) 847-851
12. Liu H.M. Generalized variational principles for ion acoustic plasma waves by He's semi-inverse method. Chaos, Solitons and Fractals 23 (2005) 573-576
13. He J.H., and Wu X.H. Exp-function method for nonlinear wave equations. Chaos, Solitons and Fractals 30 3 (2006) 700-708
14. J.H. He, M.A. Abdou, New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos, Solitons and Fractals, in press (doi: 10.1016/j.chaos.2006.05.072)
15. Wazwaz A.M. The tanh method: Solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations. Chaos, Solitons and Fractals 25 (2005) 55-63
16. Abdusalam H.A. On an improved complex tanh-function method. International Journal of Nonlinear Science and Numerical Simulation 6 (2005) 99-106
17. El-Sabbagh M.F., and Ali A.T. New exact solutions for (3 + 1)-dimensional Kadomtsev-Petviashvili equation and generalized (2 + 1)-dimensional Boussinesq equation. International Journal of Nonlinear Science and Numerical Simulation 6 (2005) 151-162
18. Bai C.L., and Zhao H. Generalized extended tanh-function method and its application. Chaos, Solitons and Fractals 27 (2006) 1026-1035
19. Abdou M.A., and Soliman A.A. Modified extended tanh-function method and its application on nonlinear physical equations. Physics Letters A 353 6 (2006) 487-492
20. Ibrahim R.S., and El-Kalaawy O.H. Extended tanh-function method and reduction of nonlinear Schrödinger-type equations to a quadrature. Chaos, Solitons and Fractals 31 4 (2007) 1001-1008
21. El-Wakil S.A., and Abdou M.A. New exact travelling wave solutions using modified extended tanh-function method. Chaos, Solitons and Fractals 31 4 (2007) 840-852
22. Elwakil S.A., El-Labany S.K., Zahran M.A., and Sabry R. Modified extended tanh-function method and its applications to nonlinear equations. Applied Mathematics and Computation 161 2 (2005) 403-412
23. Lü Z., and Zhang H. Applications of a further extended tanh method. Applied Mathematics and Computation 159 2 (2004) 401-406
24. Pedit F., and Wu H. Discretizing constant curvature surfaces via loop group factorizations: The discrete sine- and sinh-Gordon equations. Journal of Geometry and Physics 17 3 (1995) 245-260
25. Wazwaz A.M. Exact solutions to the double sinh-Gordon equation by the tanh method and a variable separated ODE method. Computers & Mathematics with Applications 50 10-12 (2005) 1685-1696
26. Zhao X., Wang L., and Sun W. The repeated homogeneous balance method and its applications to nonlinear partial differential equations. Chaos, Solitons and Fractals 28 2 (2006) 448-453
27. Zhaosheng F. Comment on "On the extended applications of homogeneous balance method". Applied Mathematics and Computation 158 2 (2004) 593-596
28. Zhang J.-F. Homogeneous balance method and chaotic and fractal solutions for the Nizhnik-Novikov-Veselov equation. Physics Letters A 313 5-6 (2003) 401-407
29. Zhao X., and Tang D. A new note on a homogeneous balance method. Physics Letters A 297 1-2 (2002) 59-67
30. Zhang J.L., Wang M.L., Wang Y.M., et al. The improved F-expansion method and its applications. Physics Letters A 350 (2006) 103-109
31. Fan E., and Zhang J. Applications of the Jacobi elliptic function method to special-type nonlinear equations. Physics Letters A 305 6 (2002) 383-392
32. Hon Y.C., and Fan E. Uniformly constructing finite-band solutions for a family of derivative nonlinear Schrödinger equations. Chaos, Solitons and Fractals 24 4 (2005) 1087-1096
33. Yomba E. The extended Fan's sub-equation method and its application to KdV-MKdV, BKK and variant Boussinesq equations. Physics Letter A 336 (2005) 463-476
34. Yomba E. The modified extended Fan sub-equation method and its application to (2 + 1)-dimensional dispersive long wave equation. Chaos, Solitons and Fractals 26 (2005) 785-794
35. He J.H. Non-perturbative methods for strongly nonlinear problems (2006), Dissertation de-Verlag im Internet GmbH, Berlin
36. He J.H. Some asymptotic methods for strongly nonlinear equations. International Journal of Modern Physics B 20 (2006) 1141-1199