The extended tanh-method for finding traveling wave solutions of nonlinear evolution equations

Applied Mathematics E - Notes

Volumn 10, Issue , 2010, Pages 235-245

  Zayed, Elsayed M E ^a   Abdel Rahman, Hanan M ^b  

^a Zagazig University   (Egypt)

^b HIGHER TECHNOLOGICAL INSTITUTE   (Egypt)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 78650713427     PISSN: 16072510     EISSN: 16072510     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. H. Segur and M. J. Ablowitz, Solitons and Inverse Scattering Transform, Philadelphia: SIAM; 1981.
2. F. Pempinelli, M. Manna, J. J. P. Leon and M. Boiti, On the spectral transform of the Korteweg-de Vries equation in two spatial dimensional, Inverse Probl., 2(1986), 271-279.
3. M. A. Abdou and S. A. El-Wakil, New exact traveling wave solutions using modified extended tanh function method, Chaos Soliton Fractal, 31(2007), 840-852.
4. E. G. Fan, Uniformly constructing a series of explicit exact solutions to nonlinear equations in mathematical physics, Chaos Solitons Fractals, 16(2003), 819-839.
5. H. Zhang and E. Fan, A note on the homogeneous balance method, Phys. Lett. A, 264(1998), 403-406.
6. E. Fan, Extended tanh function method and its applications to nonlinear equations, Phys. Lett. A, 277(2002), 212-218.
7. R. Hirota, Direct method of finding exact solutions of nonlinear evolution equations, In: Bullough R, Caudrey P, editors. B̈acklund tansformations, Berlin: Springer; (1980) 1157-1175.
8. K. Miodek and M. Jaulent, Nonlinear evolution equations associated with energy dependent Schrodinger potentials, Lett. Math. Phys., 1(1976), 243-250.
9. S. Y. Lou, On the coherent structures of the Nizhnik Novikov Veselov equation, Phys. Lett. A, 277(2000), 94-100.
10. W. Malfliet, Solitory wave solutions of nonlinear wave equations, Am. J. Phys., 60(1992), 650-654.
11. W. Hereman and W. Malfliet, The tanh method I: exact solutions of nonlinear evolution and wave equations, Phys. Scripta, 54(1996), 563-568.
12. Y. Matsuna, Reduction of dispersionless coupled KdV equations to the Euler-Darboux equation, J. Math. Phys., 42(2001), 1744-1760.
13. A. J. Morrison, E. J. Parkes and V. O. Vakhnenko, A B̈acklund transformation and the inverse scattering transform method for the generalised Vakhnenko equation, Chaos Soliton Fractal, 17(2003), 683-692.
14. H. Q. Zhang and Y. J. Ren, A generalized F-expansion method to find abundant families of Jacobi Ellipitic function solutions of the (2+1)-dimensional Nizhnik Novikov Veselov, Chaos Solitons Fractal, 27(2006), 959-979.
15. Z. Yan, Abundant families of Jacobi elliptic function solutions of the (2+1)- dimensional integrable Davey-Stewartson-type equation via a new method, Chaos Soliton Fractal, 18(2003), 299-309.
16. A. Bakir and E. Yusufoglu, Exact solutions of nonlinear evolution equations, Chaos Solitons Fractals, 37(2008), 842-848.
17. A. M. Wazwaz, The tanh method for traveling wave solutions of nonlinear equations, Appl. Math. Comput., 154(2004), 713-723.
18. A. M. Wazwaz, Traveling wave solutions of generalized forms of Burger, Burger-KdV and Burger-Huxley equations, Appl. Math. Comput.,169(2005), 639-656.
19. A. M. Wazwaz, The tanh method: exact solutions of the Sine-Gordon and Sinh-Gordon equations, Appl. Math. Comput., 167(2005), 1196-1210.
20. A. M. Wazwaz, The tanh method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations, Chaos Soliton Fractal, 25(2005), 55-63.
21. A. M. Wazwaz, The extended tanh method for new soliton solutions for many forms of the fifth-order KdV equations, Appli. Math. Comput. 184(2007), 1002-1014.
22. A. M. Wazwaz, New solitary wave solutions to modified forms of Degasperis-Procesi and Camassa-Holm equations, Appl. Math. Comput., 186(2007), 130-141.
23. H. Q. Zhang, B. Li and T. C. Xia, new explicit and exact solutions for the Nizhnik-Novikov-Veselov equation, Appl. Math. E. Notes, 1(2001), 139-142.
24. Y. P. Zheng, Separability and dynamical r-matrix for the constrainted flows of the Jaulent Miodek hierarchy, Phys. Lett. A, 216(1996), 26-32.
25. R. G. Zhou, The finite band solution of the Jaulent Miodek equation, J. Math. Phys. 38(1999), 2535-2546.