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Comparison of solutions of mKdV equation by using the first integral method and (G′ G )-expansion method

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Abstract (2. Language): 
The first integral method and the (G′ G )-expansion method are two efficient methods for obtaining exact solutions of some nonlinear partial differential equations. In this paper, we first describe the first integral method and the (G′ G )- expansion method. Then we solve the mKdV equation with both meth- ods and compare the solutions.
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REFERENCES

References: 

[1] M.Ablowitz, P.A. Clarkson, Soliton Nonlinear Evolution Equation and
Inverse Scattering, Cambrridge University Press, New York, 1991.
[2] M.Wadati, Wave Propagation in nonlinear lattice, J. Phys. Soc. Jpn.
1975, 38, 673− 680.
[3] M.R. Miura, Backlund Transformation, Spring-Verlag,Berlin, 1978.
[4] V.A. Matveev, M.A. Salle, Darboux Transformation and Solitons, Spring-
Verlag,Berlin, Heidelberg, 1991.
[5] C.H.Gu et al, Darboux Transformation in Solitons Theory and Geometry
Applications, Shangai Science Technology Press, Shanghai, 1999.
[6] Ryogo Hirota, Exact Solution of the Korteweg-de Vries Equation for Mu-
tiple Collisions of Solitons, Phys. Rev. Lett. 1971, 27, 192− 1194.
[7] Ryogo Hirota, The Direct Method in Soliton Theory, Cambridge Univer-
sity Press, 2004.
[8] M.L.Wang, Solitary wave solutions for vaiant Boussinesq equations, Phys.
Lett. A 1995, 199, 169− 172.
[9] E.G. Fan, H.Q.Zhang, A note on the homogeneous balance method, Phys.
Lett. A 1998, 246, 403− 406.
[10] Y.Cheng, Q. Wang, A new general algebraic method with symbolic
computation to construct new travelling wave solution for the (1 +
1)-dimensional dispersive long wave equation, Appl. Math. Comput.
2005, 168, 1189− 1204.
[11] E.G. Fan, Extended tanh-function method and its applications to nonlin-
ear equations, Phys. Lett. A 2000, 277, 212− 218.
[12] Z.Y. Yan, New explicit travelling wave solutions for two new integrable
coupled nonlinear evolution equations, Phys. Lett. A 2001, 292, 100−106.
[13] E.G. Fan, Travelling wave solutions in terms of special functions for non-
linear coupled evolution systems,Phys. Lett. A 2002, 300, 43− 249.
320 N.Taghizadeh and M.Najand
[14] E.G. Fan, A new algebraic method for finding the line soliton solutions
and doubly periodic wave solution to a two-dimensional perturbed Kdv
equation, Chaos Solitons Fract. 2003, 15, 67− 574.
[15] M.A. Abdou, An improved generalized F-expansion method and its ap-
plications, J. Comput. Appl. Math. 2008, 214, 202− 208.
[16] Emmanuel Yomba, he modified extended Fan sub-equation method and its
application to the (2+1)-dimensional Broer-Kaup-Kupershmidt equation,
Chaos Solitons Fract. 2006, 27, 187 − 196.
[17] Z.S. Feng, The first integral method to study the Burgers-KdV equation,
J. Phys. A: Math. Gen. 2002, 35, 343 − 349.
[18] Z.S. Feng, X.H. Wang, The first integral method to the two-dimensional
Burgers-KdV equation, Phys. Lett. A 2003, 308, 173− 178.
[19] Z.S. Feng, Traveling wave behavior for a generalized fisher equation, Chaos
Solitons Fract. 2008, 38, 481− 488.
[20] K.R. Raslan, The first integral method for solving some important non-
linear partial differential equations, Nonlinear Dynam. 2008, 53, 281−286.
[21] ML. Wang, XZ Li and JL. Zhang, The (G′
G )-expansion method and trav-
elling wave solutions of nonlinear evolution equations in mathematical
physics, Phys. Lett. A 2008, 372, 417− 423.
[22] T.R. Ding and C.Z. Li, Ordinary differential equations, Peking University
Press, Peking, 1996.
[23] N. Taghizadeh, F. Farahrooz, M. Mirzazadeh, Exact solutions of Ku-
pershmidt equation by (G′
G )-expansion method, J. Comput. Appl. Math.
2010, 2(4), 32− 37.

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