Document Type : Research Paper

**Author**

University of Guilan

**Abstract**

In this paper, the modified simplest equation method is successfully implemented to find travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation. This method is direct, effective and easy to calculate, and it is a powerful mathematical tool for obtaining exact travelling wave solutions of the generalized forms $B(n,1)$ and $B(-n,1)$ of Burgers equation and can be used to solve other nonlinear partial differential equations in mathematical physics.

**Keywords**

[1] E. Fan, Extended tanh-function method and its applications to nonlinear equations,

Physics Letters A, 277(4-5) (2000) 212-218.

Physics Letters A, 277(4-5) (2000) 212-218.

[2] E. G. Fan, Extended tanh-function method and its applications to nonlinear equations,

Phys. Lett. A, 277 (2000) 212-218.

Phys. Lett. A, 277 (2000) 212-218.

[3] E. Fan and H. Zhang, A note on the homogeneous balance method, Phys. Lett. A, 246

(1998) 403-406.

(1998) 403-406.

[4] J. H. He and X.H. Wu, Exp-function method and for nonlinear wave equations. Chaos,

Solitons and Fractals, 30 (2006) 700-708.

Solitons and Fractals, 30 (2006) 700-708.

[5] A. J. M. Jawad, M. D. Petkovic and A. Biswas, Modied simple equation method for

nonlinear evolution equations, Appl. Math. Comput., 217 (2010) 869-877.

nonlinear evolution equations, Appl. Math. Comput., 217 (2010) 869-877.

[6] S. K. Liu, Z. T. Fu, S. D. Liu and Q. Zhao, Jacobi elliptic function expansion method

and periodic wave solutions of nonlinear wave equatins, Phys. Lett. A, 289 (2001) 72-76.

and periodic wave solutions of nonlinear wave equatins, Phys. Lett. A, 289 (2001) 72-76.

[7] N. K. Vitanov, Z. I. Dimitrova and H. Kantz, Modied method simplest equation and

application to nonlinear PDFs, Appl. Math. Comput., 216 (2010) 2587-2595.

application to nonlinear PDFs, Appl. Math. Comput., 216 (2010) 2587-2595.

[8] N. K. Vitanov, Modied method simplest equation poerful tool for obtaining exact

and approximate traveling-wave solutions of nonlinear PDFs, Commun Nonlinear. Sci.

Numer. Simulat., 16 (2011) 1179-1185.

and approximate traveling-wave solutions of nonlinear PDFs, Commun Nonlinear. Sci.

Numer. Simulat., 16 (2011) 1179-1185.

[9] N. K. Vitanov and Z. I. Dimitrova, Application of the method of simplest equation for

obtaining exact traveling-wave solutions for two classes of model PDFs from ecoloy and

population dynamics. Commun. Nonlinear Sci. Numer. Simulat., 15 (2010) 2836-2845.

obtaining exact traveling-wave solutions for two classes of model PDFs from ecoloy and

population dynamics. Commun. Nonlinear Sci. Numer. Simulat., 15 (2010) 2836-2845.

[10] M.Wang, X. Li and J. Zhang, The (G′

G )-expansion method and travelling wave solutions

of nonlinear evolution equations in mathematical physics, Phys. Lett. A, 372 (2008) 417-

423.

G )-expansion method and travelling wave solutions

of nonlinear evolution equations in mathematical physics, Phys. Lett. A, 372 (2008) 417-

423.

[11] M. L. Wang and X. Z. Li, Applications of F-expansion to periodic wave solutions for a

new Hamiltonian amplitude equation, Chaos Soliton Fract., 24 (2005) 1257-1268.

new Hamiltonian amplitude equation, Chaos Soliton Fract., 24 (2005) 1257-1268.

[12] E. M. E. Zayed, A note on the modied simple equation method applied to Sharma-

Tasso-Olver equation, Appl. Math. Comput., 218 (2011) 3962-3964.

Tasso-Olver equation, Appl. Math. Comput., 218 (2011) 3962-3964.

[13] E. M. E. Zayed and S.A.H. Ibrahim, Exact solutions of nonlinear evolution equations

in mathematical physics using the modied simple equation method, chinese physics

Letters, 29(6) (2012), Article ID 060201.

in mathematical physics using the modied simple equation method, chinese physics

Letters, 29(6) (2012), Article ID 060201.

[14] H. Zhang, New application of the (G′,G )-expansion method, Commun. Nonlinear Sci.

Numer. Simul., 14 (2009) 3220-3225.

Numer. Simul., 14 (2009) 3220-3225.

Summer 2013

Pages 71-77

**Receive Date:**17 December 2013**Accept Date:**17 December 2013