The tanh and the sine-cosine methods for exact solutions of the MBBM and the Vakhnenko equations

Chaos, Solitons and Fractals

Volumn 38, Issue 4, 2008, Pages 1126-1133

  Yusufoglu E ^a   Bekir, A ^a  

^a DUMLUPINAR UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

SOLITONS;

EXACT SOLUTION; EXACT TRAVELLING WAVE SOLUTIONS; NONLINEAR EVOLUTION EQUATION; PERIODIC SOLUTION; SINE-COSINE METHODS; SOLITON SOLUTIONS; VAKHNENKO EQUATION;

NONLINEAR EQUATIONS;

EID: 45849111860     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2007.02.004     Document Type: Article

References (28)

1. Ablowitz M.J., and Segur H. Solitons and inverse scattering transform (1981), SIAM, Philadelphia
2. Benjamin T.B., Bona J.L., and Mahony J.J. Model equations for long waves in nonlinear dispersive systems. Philos Trans Roy Soc London Ser A 272 (1972) 47-48
3. El-Wakil S.A., and Abdou M.A. New exact travelling wave solutions using modified extended tanh-function method. Chaos, Solitons & Fractals 31 4 (2007) 840-852
4. El-Wakil S.A., and Abdou M.A. Modified extended tanh-function method for solving nonlinear partial differential equations. Chaos, Solitons & Fractals 31 5 (2007) 1256-1264
5. Fan E., and Zhang H. A note on the homogeneous balance method. Phys Lett A 246 (1998) 403-406
6. Fan E. Extended tanh-function method and its applications to nonlinear equations. Phys Lett A 277 (2000) 212
7. Fan E., and Hon Y.C. Generalized tanh method extended to special types of nonlinear equations. Z Naturforsch 57a (2002) 692-700
8. Hirota R. Direct method of finding exact solutions of nonlinear evolution equations. In: Bullough R., and Caudrey P. (Eds). Backlund transformations (1980), Springer, Berlin 1157-1175
9. Malfliet W. Solitary wave solutions of nonlinear wave equations. Am J Phys 60 (1992) 650-654
10. Khater A.H., Malfliet W., Callebaut D.K., and Kamel E.S. The tanh method, a simple transformation and exact analytical solutions for nonlinear reaction-diffusion equations. Chaos, Solitons & Fractals 14 2 (2002) 513-522
11. Tso T. Existence of solutions of the modified Benjamin-Bone-Mahony equation. Chin J Math 24 4 (1996) 327-336
12. Vakhnenko V.O., and Parkes E.J. The two loop soliton of the Vakhnenko equation. Nonlinearity 11 (1998) 1457-1464
13. Vakhnenko V.O., and Parkes E.J. The calculation of multi-soliton solutions of the Vakhnenko equation. Chaos, Soliton & Fractals 13 (2002) 1819-1826
14. Vakhnenko V.O., Parkes E.J., and Morrison A.J. A B äcklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation. Chaos, Solitons & Fractals 17 4 (2003) 683-692
15. Yan Z. Constructing exact solutions for two-dimensional nonlinear dispersion Boussinesq equation II: solitary pattern solutions. Chaos, Solitons & Fractals 18 4 (2003) 869-880
16. Yan Z. Abundant families of Jacobi elliptic function solutions of the (2 + 1)-dimensional integrable Davey-Stewartson-type equation via a new method. Chaos, Solitons & Fractals 18 2 (2003) 299-309
17. Yusufoglu E., and Bekir A. Exact Solutions of Coupled Nonlinear Evolution Equations. Chaos, Solitons & Fractals 37 3 (2008) 842-848
18. Yusufoglu E., Bekir A., and Alp M. Periodic and solitary wave solutions of Kawahara and modified Kawahara equations by using Sine-Cosine method. Chaos, Solitons & Fractals 37 4 (2008) 1193-1197
19. Wadati M. Introduction to solitons. Pramana: J Phys 57 5-6 (2001) 841-847
20. Wadati M. The exact solution of the modified Korteweg-de Vries equation. J Phys Soc Jpn 32 (1972) 1681-1687
21. Wadati M. The modified Korteweg-de Vries equation. J Phys Soc Jpn 34 (1973) 1289-1296
22. Wazwaz A.M. Two reliable methods for solving variants of the KdV equation with compact and noncompact structures. Chaos, Solitons & Fractals 28 2 (2006) 454-462
23. Wazwaz A.M. The tanh method: exact solutions of the Sine-Gordon and Sinh-Gordon equations. Appl Math Comput 167 (2005) 1196-1210
24. Wazwaz A.M. The tanh method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations. Chaos, Solitons & Fractals 25 1 (2005) 55-63
25. Wazwaz A.M. The sine-cosine method for obtaining solutions with compact and noncompact structures. Appl Math Comput 159 2 (2004) 559-576
26. Wazwaz A.M., and Helal M.A. Nonlinear variants of the BBM equation with compact and noncompact physical structures. Chaos, Solitons & Fractals 26 3 (2005) 767-776
27. Wazwaz A.M. New compactons, solitons and periodic solutions for nonlinear variants of the KdV and the KP equations. Chaos, Solitons & Fractals 22 1 (2004) 249-260
28. Wazwaz A.M. A sine-cosine method for handling nonlinear wave equations. Math Comput Model 40 (2004) 499-508