Skip to content
IJAMR International Journal of Applied Mathematical Research E-ISSN 2227-4324

Application of G'/G expansion method to two concert problems

Authors and Affiliations

  • Zeinab Ayati
  • Jafar Biazar

About this article

Download PDF

Abstract

In this work G'/G expansion method is used to obtain exact solutions of the Jimbo-Miwa (JM) and Tzitzeica-Dodd_Bullough (TDB) equations. It is shown that G'/G expansion method is straightforward and concise, and its applications are promising.

References

[1] A.M. Wazwaz, The tanh method: Exact solutions of the Sine–Gordon and Sinh– Gordon equations, Applied Mathematics and Computation 167 (2005)1196–1210.

[2] Malfliet W, Hereman W. The tanh method: I. Exact solutions of nonlinear evolution and wave equations, Physica Scripta 54 (1996) 563–8.

[3] Wazwaz AM. The tanh and the sine–cosine methods for a reliable treatment of the modified equal width equation and its variants, Communications in Nonlinear Science and Numerical Simulation 11 (2006) 148–60.

[4] J. Biazar, H. Ghazvini, Exact solutions for non-linear Schrödinger equations by He’s homotopy perturbation method, Physics Letters A 366 (2007) 79-84.

[5] J.H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals 26(2005) 695–700.

View more references (17)

[6] J.H. He, Variational iteration method—a kind of non-linear analytical technique: some examples, International Journal of Non-Linear Mechanics 34 (1999) 699–708.

[7] J.H. He, Variational iteration method for autonomous ordinary differential systems, Applied Mathematics and Computation 114 (2000) 115–123.

[8] J. Biazar, E. Babolian, A. Nouri, R. Islam, An alternate algorithm for computing Adomian Decomposition method in special cases, Applied Mathematics and Computation 38 (2-3) (2003) 523- 529.

[9] J.H. He, X.H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fractals 30 (2006) 700–708.

[10] S. Zhang, Application of Exp-function method to a KdV equation with variable coefficients, Physics Letters A 365(2007) 448–453.

[11] J. Biazar, z. ayati, Application of Exp-function method to Equal-width wave equation, Physica Scripta (2008) 78 045005.

[12] M.L. Wang, Exact solutions for a compound KdV-Burgers equation, Physics Letters A 213 (1996) 279.

[13] M.A. Abdou, The extended F-expansion method and its application for a class of nonlinear evolution equations, Chaos Solitons Fractals 31 (2007) 95-104.

[14] M.L. Wang, X.Z. Li, J.L. Zhang, The expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A 372 (2008) 417–423.

[15] M. Jimbo, T. Miwa, Solitons and infinite-dimensional Lie algebras, Publ. Res. Inst. Math. Sci. 19 (1983) 943.

[16] W.X. Ma, Comment on "Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation, Journal of Mathematical Physics 40 (1999) 3685.

[17] B. Dorizzi, B. Grammaticos, A. Ramani, P. Winternitz, Are all the equations of the Kadomtsev-Petviashvili hierarchy integrable?, Journal of Mathematical Physics 27 (1986) 2848.

[18] S.Y. Lou, J.P. Weng, Generalized W∞ symmetry algebra of the conditionally integrable nonlinear evolution equation, Journal of Mathematical Physics 36 (1995) 3492

[19] A.M. Wazwaz, New solutions of distinct physical structures to high-dimensional nonlinear evolution equations, Applied Mathematics and Computation 196 (2008) 363

[20] A.M. Wazwaz, Multiple-soliton solutions for the Calogero–Bogoyavlenskii–Schiff, Jimbo–Miwa and YTSF equations, Applied Mathematics and Computation 203 (2) (2008) 592

[21] A.M.Wazwaz, The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations, Chaos, Solitons & Fractals 2005;25(1):55–65

[22] J.H. He, M.A. Abdou New periodic solutions for nonlinear evolution equations using Exp-function method, Chaos, Solitons and Fractals 34 (2007) 1421–1429.


How to Cite

Ayati, Z., & Biazar, J. (2012). Application of G’/G expansion method to two concert problems. International Journal of Applied Mathematical Research, 2(1), 49-54. https://doi.org/10.14419/ijamr.v2i1.456