International Science Index


Traveling Wave Solutions for the Sawada-Kotera-Kadomtsev-Petviashivili Equation and the Bogoyavlensky-Konoplechenko Equation by (G'/G)- Expansion Method


This paper presents a new function expansion method for finding traveling wave solutions of a nonlinear equations and calls it the G G -expansion method, given by Wang et al recently. As an application of this new method, we study the well-known Sawada-Kotera-Kadomtsev-Petviashivili equation and Bogoyavlensky-Konoplechenko equation. With two new expansions, general types of soliton solutions and periodic solutions for these two equations are obtained.

[1] M. Wang, Y. Zhou and Z. Li, Application of a homogeneous balance method to exact solutions of nonlinear equations in mathematical physics, Physics Letters A, vol. 216, 1996, pp. 67-75.
[2] X. Zhao, L. Wang and W. Sun, The repeated homogeneous balance method and its applications to nonlinear partial differential equations, Chaos, Solitions and Fractals, vol. 28, 2006, pp. 448-453.
[3] A. M. Wazwaz, New solitary wave and periodic wave solutions to the (2+1)-dimensional Nizhnik-Nivikov-veselov system, Applied Mathematics Computation, vol. 187, 2007, pp. 1584-1591.
[4] M. Wang, Solitary wave solutions for variant Boussinesq equations, Physics Letters A, vol. 199, 1995, pp. 169-172.
[5] W, Malfielt and W. Hereman, The tanh method: I. Exact solutions of nonlinear evolution and wave equations, Physica Scripta, vol. 54, 1996, pp. 563-568.
[6] V. A. Arkadiev and A. K. Pogrebkov, Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation, Physica D: Nonlinear Phenomena, vol. 36, 1989, pp. 189-197.
[7] Y. Matsuno, B¨acklund transformation, conservation laws, and inverse scattering transform of a model integrodifferential equation for water waves, Journal of Mathematical Physics, vol. 31, 1990, pp. 2904-2917.
[8] J. M. Zho and Y. M. Zhang, The Hirota bilinear method for the coupled Burgers equation and the high-order Boussinesq Burgers equation, Chinese Physics B, vol. 20, 2010, pp. 010205.
[9] M. A. Abdou, Multiple Kink Solutions and Multiple Singular Kink Solutions for (2+1)-dimensional Integrable Breaking Soliton Equations by Hirota-s Method, Studies in Nonlinear Science, vol. 2, 2011, pp. 1-4.
[10] M. A. Abdou, An Extended Riccati Equation Rational Expansion Method and its Applications, International Journal of Nonlinear Science, vol. 7, 2009, pp. 57-66.
[11] X. L. Zhang, J. Wang and N. Q. Zhang, J. Wang and N. Q. Zhang, A New Generalized Riccati Equation Rational Expansion Method to Generalized BurgersFisher Equation with Nonlinear Terms of Any Order, Communication in Theoretical Physics, vol. 46, 2006, pp. 779-786.
[12] J. P. Yu and Y. L. Sun, Weierstrass Elliptic Function Solutions to Nonlinear Evolution Equations, Communication in Theoretical Physics, vol. 50, 2008, pp. 295-298.
[13] Z. Y. Yan, New Doubly Periodic Solutions of Nonlinear Evolution Equations via Weierstrass Elliptic Function Expansion Algorithm, Communication in Theoretical Physics, vol. 42, 2004, pp. 645-648.
[14] A. M. Wazwaz, A sine-cosine method for handlingnonlinear wave equations, Mathematical and Computer Modelling, vol. 40, 2004, pp. 499-508.
[15] M. Alquran and K. Al-Khaled, The tanh and sinecosine methods for higher order equations of Kortewegde Vries type, Physica Scripta, vol. 84, 2011, pp. 025010.
[16] S. Zhang and H. Q. Zhang, Discrete Jacobi elliptic function expansion method for nonlinear differential-difference equations, Physica Scripta, vol. 80, 2009, pp. 045002.
[17] W. Zhang, Extended Jacobi Elliptic Function Expansion Method to the ZK-MEW Equation, International Journal of Differential Equations, vol. 2011, 2011, pp. 451420.
[18] A. A. Mohammad and M. Can, Painleve Analysis and Symmetries of the HirotaSatsuma Equation, Nonlinear Mathematical Physics, vol. 3, 1996, pp. 152-155.
[19] N. Goyal and R. K. Gupta, Symmetries and exact solutions of non diagonal Einstein-Rosen metrics, vol. 85, 2012, pp. 015004.
[20] M. Wang, X. Li, J. Zhang, The (G'/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, Physics Letters A, vol. 372, 2008, pp. 417-428.
[21] X. Liu, W. Zhang and Z. Li, Applications of improved (G'/G)-expansion method to traveling wave solutions of two nonlinear evolution equations, Advances in Applied Mathematics and Mechanics, vol. 4, 2010, pp. 122-130.
[22] K. A. Gapreel, A Generalized (G'/G)-expansion method to find the traveling wave solutions of nonlinear evolution equations, Journal of Partial Differential Equations, vol. 24, 2011, pp. 55-69.
[23] Y. B. Zhou, C. Li, Application of Modified (G'/G)-expansion method to traveling wave solutions for Whitham Broer Kaup-Like equations, Communication in Theoretical Physics, vol. 51, 2009, pp. 664-670.