### Solution of Fifth Order Caudrey-Dodd-Gibbon-Sawada-Kotera Equation by the Alternative (G'/G)-Expansion Method with Generalized Riccati Equation

#### Abstract

In the present paper, the alternative (*G*'/*G*)-expansion is used to find new and precise solutions of Caudrey-Dodd-Gibbon-Sawada-Kotera equation with the assist of symbolic computation Maple, in which the generalized Riccati equation is used as an auxiliary equation. Plentiful traveling wave solutions including; exponential, hyperbolic and trigonometric functions are successfully accomplished by the proposed method with capricious parameters. It is revealed that the proposed method is straightforward, constructive and many nonlinear evolution equations in mathematical physics are solved by this method.

doi:10.14456/WJST.2015.44

#### Keywords

#### Full Text:

PDF#### References

S Liu, Z Fu, SD Liu and Q Zhao. Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations. Phys. Lett. A 2001; 289, 69-74.

W Malfliet. The tanh method: A tool for solving certain classes of nonlinear evolution and wave equations. J. Comput. Appl. Math. 2004; 164-165, 529-41.

MA Abdou. The extended tanh-method and its applications for solving nonlinear physical models. Appl. Math. Comput. 2007; 190, 988-96.

MJ Ablowitz and PA Clarkson. Solitons, Nonlinear Evolution Equations and Inverse Scattering Transform. Cambridge University Press, Cambridge, 1991.

R Hirota. Exact solution of the KdV equation for multiple collisions of solutions. Phys. Rev. Lett. 1971; 27, 1192-4.

C Rogers and WF Shadwick. Bäcklund Transformations. Academic Press, New York, 1982.

JH He and XH Wu. Exp-function method for nonlinear wave equations. Chaos Soliton. Fract. 2006; 30, 700-8.

H Naher, FA Abdullah and MA Akbar. New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the Exp-function method. J. Appl. Math. 2012; 2012, Article ID 575387.

ST Mohyud-Din, MA Noor and A Waheed. Exp-function method for generalized traveling solutions of Calogero-Degasperis-Fokas equation. Z. Naturforsch. J. Phy. Sci. 2010; 65, 78-84.

NA Kudryashov. On types of nonlinear non-integrable equations with exact solutions. Phys. Lett. A 1991; 155, 269-75.

MA Abdou and AA Soliman. Modified extended tanh-function method and its application on nonlinear physical equations. Phys. Lett. A 2006; 353, 487-92.

X Zhao, L Wang and W Sun. The repeated homogeneous balance method and its applications to nonlinear partial differential equations. Chaos Soliton. Fract. 2006; 28, 448-53.

M Wang, X Li and J Zhang. The (G'/G)-expansion method and traveling wave solutions of nonlinear evolution equations in mathematical physics. Phys. Lett. A 2008; 372, 417-23.

MA Akbar, NHM Ali and ST Mohyud-Din. The alternative (G'/G)-expansion method with generalized Riccati equation: Application to fifth order (1+1)-dimensional Caudrey-Dodd-Gibbon equation. Int. J. Phys. Sci. 2012; 7, 743-52.

MA Akbar, NHM Ali and EME Zayed. Abundant exact traveling wave solutions of the generalized Bretherton equation via the improved (G'/G)-expansion method. Comm. Theor. Phys. 2012; 57, 173-8.

MA Akbar and NHM Ali. The alternative (G'/G)-expansion method and its applications to nonlinear partial differential equations. Int. J. Phys. Sci. 2011; 6, 7910-20.

MA Akbar, NHM Ali and EME Zayed. A generalized and improved (G'/G)-expansion method for nonlinear evolution equations. Math. Probl. Eng. 2012; 2012, Article ID 459879.

J Zhang, F Jiang and X Zhao. An improved (G'/G)-expansion method for solving nonlinear evolution equations. Int. J. Comput. Math. 2010; 87, 1716-25.

EME Zayed. New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized (G'/G)-expansion method. J. Phys. A Math. Theor. 2009; 42, 195202-14.

EME Zayed. The (G'/G)-expansion method combined with the Riccati equation for finding exact solutions of nonlinear PDEs. J. Appl. Math. Inform. 2011; 29, 351-67.

S Zhu. The generalized Riccati equation mapping method in non-linear evolution equation: application to (2+1)-dimensional Boiti-Leon-Pempinelle equation. Chaos Soliton. Fract. 2008; 37, 1335-42.

WL Chan and YK Zheng. Bäcklund transformations for the Caudrey-Dodd-Gibbon-Sawada-Kotera equation and its λ-modified equation. J. Math. Phys. 1989; 30, 2065-8.

### Refbacks

- There are currently no refbacks.

**Online ISSN: 2228-835X****http://wjst.wu.ac.th **

**Last updated:**18 January 2018