Exact and explicit solutions to some nonlinear evolution equations by utilizing the (G′/G)-expansion method

Applied Mathematics and Computation

Volumn 215, Issue 2, 2009, Pages 857-863

  Aslan, Ismail ^a  

^a IZMIR INSTITUTE OF TECHNOLOGY   (Turkey)

Author keywords

(G G) expansion method; Burgers KdV equation; Modified Benjamin Bona Mahony equation; Modified Degasperis Procesi equation; Traveling wave solutions

Indexed keywords

BURGERS-KDV EQUATION; EXPANSION METHODS; EXPLICIT SOLUTIONS; MODIFIED BENJAMIN-BONA-MAHONY EQUATION; MODIFIED DEGASPERIS-PROCESI EQUATION; NONLINEAR EVOLUTION EQUATION; SOLITARY WAVE; SYMBOLIC COMPUTATION; TRAVELING WAVE SOLUTIONS;

COMPUTATIONAL MECHANICS; DIFFERENTIAL EQUATIONS; SET THEORY;

NONLINEAR EQUATIONS;

EID: 68949149900     PISSN: 00963003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.amc.2009.05.038     Document Type: Article

References (47)

1. Liu G.T., and Fan T.Y. New applications of developed Jacobi elliptic function expansion methods. Phys. Lett. A 345 (2005) 161-166
2. Ablowitz M.J., and Segur H. Solitons and Inverse Scattering Transform (1981), SIAM, Philadelphia
3. Hirota R. The Direct Method in Soliton Theory (2004), Cambridge University Press, Cambridge
4. Wang M.L. Exact solutions for a compound KdV-Burgers equation. Phys. Lett. A 213 (1996) 279-287
5. He J.H. The homotopy perturbation method for nonlinear oscillators with discontinuities. Appl. Math. Comput. 151 (2004) 287-292
6. Yan Z.Y. An improved algebra method and its applications in nonlinear wave equations. Chaos Solitons Fractals 21 (2004) 1013-1021
7. Bluman G.W., and Kumei S. Symmetries and Differential Equations (1989), Springer-Verlag, New York
8. Adomian G. Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer, Boston
9. Yan C.T. A simple transformation for nonlinear waves. Phys. Lett. A 224 (1996) 77-84
10. Malfliet W., and Hereman W. The tanh method I: Exact solutions of nonlinear evolution and wave equations. Phys. Scr. 54 (1996) 563-568
11. Abdou M.A. The extended F-expansion method and its application for a class of nonlinear evolution equations. Chaos Solitons Fractals 31 (2007) 95-104
12. He J.H., and Wu X.H. Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30 (2006) 700-708
13. Öziş T., and Aslan I. Exact and explicit solutions to the (3 + 1)-dimensional Jimbo-Miwa equation via the Exp-function method. Phys. Lett. A 372 (2008) 7011-7015
14. Wang M., Li X., and Zhang J. The (G′/G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 372 (2008) 417-423
15. Bekir A. Application of the (G′/G)-expansion method for nonlinear evolution equations. Phys. Lett. A 372 (2008) 3400-3406
16. A. Bekir, A.C. Cevikel, New exact travelling wave solutions of nonlinear physical models, Chaos Solitons Fractals, doi:10.1016/j.chaos.2008.07.017.
17. E.M.E. Zayed, K.A. Gepreel, Some applications of the (G′/G)-expansion method to non-linear partial differential equations, Appl. Math. Comput., doi:10.1016/j.amc.2009.02.009.
18. Ganji D.D., and Abdollahzadeh M. Exact traveling solutions of some nonlinear evolution equation by (G′/G)-expansion method. J. Math. Phys. 50 (2009) 013519
19. Wang M., Zhang J., and 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. 206 (2008) 321-326
20. Ling-Xiao L., and Ming-Liang W. The (G′/G)-expansion method and travelling wave solutions for a higher-order nonlinear schrödinger equation. Appl. Math. Comput. 208 (2009) 440-445
21. Zayed E.M.E., and Gepreel K.A. The (G′/G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics. J. Math. Phys. 50 (2008) 013502
22. Bruzon M.S., and Gandarias M.L. New exact solutions for a Benjamin-Bona-Mahony equation. Mathematics and Computers in Science and Engineering (2008) 189-194
23. Aslan I., and Öziş T. Analytic study on two nonlinear evolution equations by using the (G′/G)-expansion method. Appl. Math. Comput. 209 (2009) 425-429
24. Aslan I., and Öziş T. On the validity and reliability of the (G′/G)-expansion method by using higher-order nonlinear equations. Appl. Math. Comput. 211 (2009) 531-536
25. Öziş T., and Aslan I. Symbolic computation and construction of new exact traveling wave solutions to Fitzhugh-Nagumo and Klein-Gordon equations. Z. Naturforsch. 64a (2009) 15-20
26. Öziş T., and Aslan I. Symbolic computations and exact and explicit solutions of some nonlinear evolution equations in mathematical physics. Commun. Theor. Phys. 51 (2009) 577-580
27. Zhang J., Wei X., and Lu Y. A generalized (G′/G)-expansion method and its applications. Phys. Lett. A 372 (2008) 3653-3658
28. Zhang S., Wang W., and Tong J. A generalized (G′/G)-expansion method and its application to the (2 + 1)-dimensional Broer-Kaup equations. Appl. Math. Comput. 209 (2009) 399-404
29. Zhang S., Tong J.L., and Wang W. A generalized (G′/G)-expansion method for the mKdV equation with variable coefficients. Phys. Lett. A 372 (2008) 2254-2257
30. Zhang S., Dong L., Ba J., and Sun Y. The (G′/G)-expansion method for nonlinear differential-difference equations. Phys. Lett. A 373 (2009) 905-910
31. Yu-Bin Z., and Chao L. Application of modified (G′/G)-expansion method to traveling wave solutions for Whitham Broer Kaup-Like equations. Commun. Theor. Phys. 51 (2009) 664-670
32. Zhang H. New application of the(G′/G)-expansion method. Commun. Nonlinear Sci. Numer. Simul. 14 (2009) 3220-3225
33. Wen-An L., Hao C., and Guo-Cai Z. The (ω / g)-expansion method and its application to Vakhnenko equation. Chinese Phys. B 18 (2009) 400-404
34. Degasperis A., and Procesi M. Asymptotic integrability. In: Degasperis A., and Gaeta G. (Eds). Symmetry and Perturbation Theory (1999), World Scientific, Singapore 23-37
35. Wazwaz A.M. Solitary wave solutions for modified forms of Degasperis-Procesi and Camassa-Holm equations. Phys. Lett. A 352 (2006) 500-504
36. Biswas A., Konar S., and Zerrad E. Soliton perturbation theory for the general modified Degasperis-Procesi Camasa-Holm equation. Int. J. Mod. Math. 2 (2007) 35-40
37. Liu Z., and Ouyang Z. A note on solitary waves for modified forms of Camassa-Holm and Degasperis-Procesi equations. Phys. Lett. A 366 (2007) 377-381
38. Wang Q., and Tang M. New exact solutions for two nonlinear equations. Phys. Lett. A 372 (2008) 2995-3000
39. Johnson R.S. A non-linear equation incorporating damping and dispersion. J. Fluid Mech. 42 (1970) 49-60
40. Gibbon J.D., Radmore P., Tabor M., and Wood D. The Painlevé property and Hirota's method. Stud. Appl. Math. 72 (1985) 39-63
41. Wazwaz A.M. Travelling wave solutions of generalized forms of Burgers, Burgers-KdV and Burgers-Huxley equations. Appl. Math. Comput. 169 (2005) 639-656
42. Feng Z. The first-integral method to study the Burgers-Korteweg-de Vries equation. J. Phys. A: Math. Gen. 35 (2002) 343-349
43. 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
44. Wazwaz A.M. New travelling wave solutions of different physical structures to generalized BBM equation. Phys. Lett. A 355 (2006) 358-362
45. Biswas A., and Konar S. Soliton perturbation theory for the generalized Benjamin-Bona-Mahoney equation. Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 703-706
46. Yusufoǧlu E., and Bekir A. The tanh and the sine-cosine methods for exact solutions of the MBBM and the Vakhnenko equations. Chaos Solitons Fractals 38 (2008) 1126-1133
47. Wazwaz A.M., and Helal M.A. Nonlinear variants of the BBM equation with compact and noncompact physical structures. Chaos Solitons Fractals 26 (2005) 767-776