The (G'/G)-expansion method for Tzitzéica type nonlinear evolution equations

Mathematical and Computer Modelling

Volumn 52, Issue 9-10, 2010, Pages 1834-1845

  Abazari, Reza ^a  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

Author keywords

(G' G) expansion method; Dodd Bullough Mikhailov (DBM) equation; Hyperbolic function solutions; Trigonometric function solutions; Tzitz ica equation; Tzitz ica Dodd Bullough (TDB) equation

Indexed keywords

DODD-BULLOUGH-MIKHAILOV (DBM) EQUATION; EXACT SOLUTION; EXPANSION METHODS; NONLINEAR EVOLUTION EQUATION; SOLITARY WAVE; SYMBOLIC COMPUTATION; TRIGONOMETRIC FUNCTION SOLUTIONS;

EXPANSION; FUNCTION EVALUATION; HYPERBOLIC FUNCTIONS; SOLITONS;

NONLINEAR EQUATIONS;

EID: 77956012260     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2010.07.013     Document Type: Article

References (37)

1. Ablowitz M.J., Segur H. Solitons and Inverse Scattering Transform 1981, SIAM, Philadelphia.
2. Tam H.W., Hu X.B. Soliton solutions and Backlund transformation for the Kupershmidt five-field lattice: a bilinear approach. Appl. Math. Lett. 2002, 15:987-993.
3. Hirota R. The Direct Method in Soliton Theory 2004, Cambridge University Press, Cambridge.
4. A. Borhanifar, Reza Abazari, An unconditionally stable parallel difference scheme for telegraph equation, Math. Probl. Eng. (2009), http://doi:10.1155/2009/969610.
5. Abazari Reza, Borhanifar A. Numerical study of Burgers' and coupled Burgers' equations by differential transformation method. Comput. Math. Appl. 2010, 59:2711-2722.
6. Freeman N.C., Nimmo J.J.C. Soliton solitons of the KdV and KP equations: the Wroanskian technique. Proc. R. Soc. Lond. Ser. A 1983, 389:319-329.
7. Liu G.T., Fan T.Y. New applications of developed Jacobi elliptic function expansion methods. Phys. Lett. A 2005, 345:161-166.
8. Wang M.L. Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 1996, 213:279-287.
9. He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl. Math. Comput. 2004, 151:287-292.
10. Shahrbabaki A.Shabani, Abazari Reza Perturbation method for heat exchange between a gas and solid particles. J. Appl. Mech. Tech. Phys. 2009, 50(6):959-964.
11. Yan Z.Y. An improved algebra method and its applications in nonlinear wave equations. Chaos Solitons Fractals 2004, 21:1013-1021.
12. Bluman G.W., Kumei S. Symmetries and Differential Equations 1989, Springer-Verlag, New York.
13. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method 1994, Kluwer, Boston.
14. Yan C.T. A simple transformation for nonlinear waves. Phys. Lett. A 1996, 224:77-84.
15. Malfliet W., Hereman W. The tanh method I: exact solutions of nonlinear evolution and wave equations. Phys. Scr. 1996, 54:563-568.
16. Xu Fei Application of exp-function method to symmetric regularized long wave (SRLW) equation. Phys. Lett. A 2008, 372:252-257.
17. Tascan Filiz, Bekir Ahmet, Koparan Murat Travelling wave solutions of nonlinear evolution equations by using the first integral method. Commun. Nonlinear Sci. Numer. Simul. 2009, 14:1810-1815.
18. Wu Guo-cheng, Xia Tie-cheng A new method for constructing soliton solutions and periodic solutions of nonlinear evolution equations. Phys. Lett. A 2008, 372:604-609.
19. Wang M., Li X., Zhang J. The (G'G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 2008, 372:417-423.
20. Bekir A. Application of the (G'G)-expansion method for nonlinear evolution equations. Phys. Lett. A 2008, 372:3400-3406.
21. Aslan I., Ozis T. On the validity and reliability of the (G'G)-expansion method by using higher-order nonlinear equations. Appl. Math. Comput. 2009, 211:531-536.
22. Bekir A., Cevikel A.C. New exact travelling wave solutions of nonlinear physical models. Chaos Solitons Fractals 2009, 41:1733-1739.
23. Zayed E.M.E., Gepreel K.A. Some applications of the (G'G)-expansion method to non-linear partial differential equations. Appl. Math. Comput. 2009, 212:1-13.
24. Ganji D.D., Abdollahzadeh M. Exact traveling solutions of some nonlinear evolution equation by (G'G)-expansion method. J. Math. Phys. 2009, 50:013519.
25. Wang M., Zhang J., Li X. Application of the (G'G)-expansion to travelling wave solutions of the Broer-Kaup and the approximate long water wave equations. Appl. Math. Comput. 2008, 206:321-326.
26. Ling-Xiao L., Ming-Liang W. The (G'G)-expansion method and travelling wave solutions for a higher-order nonlinear Schrödinger equation. Appl. Math. Comput. 2009, 208:440-445.
27. Zayed E.M.E., Gepreel K.A. The (G'G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics. J. Math. Phys. 2008, 50:013502.
28. Aslan I., Ozis T. Analytic study on two nonlinear evolution equations by using the (G'G)-expansion method. Appl. Math. Comput. 2009, 209:425-429.
29. Zhang J., Wei X., Lu Y. A generalized (G'G)-expansion method and its applications. Phys. Lett. A 2008, 372:3653-3658.
30. Zhang S., Wang W., Tong J. A generalized (G'G)-expansion method and its application to the (2+1)-dimensional Broer-Kaup equations. Appl. Math. Comput. 2009, 209:399-404.
31. Yu-Bin Z., Chao L. Application of modified (G'G)-expansion method to traveling wave solutions for Whitham Broer Kaup-like equations. Commun. Theor. Phys. 2009, 51:664-670.
32. Zhang H. New application of the (G'G)-expansion method. Commun. Nonlinear Sci. Numer. Simul. 2009, 14:3220-3225.
33. Tzitzéica G. Géometric infinitésimale-sur une nouvelle classe de surface. C. R. Math. Acad. Sci. Paris 1910, 150:227.
34. El-Wakil S.A., Abdou M.A., Hendi A. New periodic wave solutions via exp-function method. Phys. Lett. A 2008, 372:830-840.
35. Wazwaz A.M. The tanh method: solitons and periodic solutions for the Dodd-Bullough-Mikhailov and the Tzitzeica-Dodd-Bullough equations. Chaos Solitons Fractals 2005, 25(1):55-63.
36. He Ji-Huan, Wu Xu-Hong Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 2006, 30:700-708.
37. He Ji-Huan, Abdou M.A. New periodic solutions for nonlinear evolution equations using exp-function method. Chaos Solitons Fractals 2007, 34:1421-1429.