Hasibun Naher and Farah Aini Abdullah. The Improved (G
/G)-Expansion Method to the (3+1)-Dimensional Kadomstev-Petviashvili Equation.
. 2013; 1(4):64-70. doi: 10.12691/AJAMS-1-4-3
expansionmethod, the Kadomstev-Petviashvili equation, traveling wave solutions, nonlinear evolution equations
This work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit
[1] | Ablowitz, M.J., Clarkson, P.A., Solitons, nonlinear evolution equations and inverse scattering. Cambridge Univ. Press, Cambridge, 1991. |
|
[2] | Hirota, R., “Exact solution of the KdV equation for multiple collisions of solutions,” Phys. Rev. Lett., 27, 1192-1194, 1971. |
|
[3] | Wang, M.L, Zhou, Y.B and Li, Z.B., “Application of homogeneous balance method to exact solutions of nonlinear equations in mathematical physics,” Phys. Lett. A, 216, 67-75, 1996. |
|
[4] | Rogers, C. and Shadwick, W.F., Backlund Transformations and their applications. Academic Press, New York, 1982. |
|
[5] | Alagesan, T., Chung, Y. and Nakkeeran, K. “Backlund transformation and soliton solutions for the coupled dispersionless equations,” Chaos, Solitons and Fractals, 21, 63-67, 2004. |
|
[6] | Liu, S., Fu, Z., Liu, S. and Zhao, Q., “Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations,” Phys. Lett. A, 289, 69-74, 2001. |
|
[7] | Malfliet, W. Solitary wave solutions of nonlinear wave equations. Am. J. Phys. 60, 650-654, 1992. |
|
[8] | Parkes, E.J. and Duffy, B.R., “An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations,” Computer Phys. Commun., 98, 288-300, 1996. |
|
[9] | Abdou, M.A., “The extended F-expansion method and its application for a class of nonlinear evolution equations,” Chaos, Solitons and Fractals, 31, 95-104, 2007. |
|
[10] | He J.H. and Wu X.H., “Exp-function method for nonlinear wave equations,” Chaos Solitons and Fractals, 30, 700-708, 2006. |
|
[11] | Naher, H., Abdullah, F.A. and Akbar, M.A., “New traveling wave solutions of the higher dimensional nonlinear partial differential equation by the Exp-function method,” J. Appl. Math. Article ID: 575387, 14 pages, 2012. |
|
[12] | Mohyud-Din, S.T., Noor, M.A. and Noor, K.I., “Exp-function method for traveling wave solutions of modified Zakharov-Kuznetsov equation,” J. King Saud Univ. 22, 213-216, 2010. |
|
[13] | Ma, W.X., Huang, T. and Zhang, Y., “A multiple exp-function method for nonlinear differential equations and its applications,” Phys. Scr. 82, 065003, 2010. |
|
[14] | Naher, H., Abdullah, F.A. and Akbar, M.A., “The exp-function method for new exact solutions of the nonlinear partial differential equations,” Int. J. Phys. Sci. 6, 6706-6716, 2011. |
|
[15] | Abbasbandy, S. and Shirzadi, A., “The first integral method for modified Benjamin-Bona-Mahony equation,” Commun. Nonlin. Science Numerical Simulation, 15, 1759-1764, 2010. |
|
[16] | Taghizadeh, N., Mirzazadeh, M. and Paghaleh, A. S., “Exact solutions for the nonlinear Schrodinger equation with power law nonlinearity,” Math. Sci. Lett., 1 (1), 7-16, 2012. |
|
[17] | Zhang, H., “New exact travelling wave solutions for some nonlinear evolution equations, part II,” Chaos, Solitons and Fractals, 37, 1328-1334, 2008. |
|
[18] | M. Noor, K. Noor, A. Waheed, and E. A. Al-Said, “An efficient method for solving system of third-order nonlinear boundary value problems,” Math. Prob. Eng., Article ID 250184, 14 pages, 2011. |
|
[19] | Plotnikov, A. V. and Skripnik, N. V., “Existence and Uniqueness Theorem for Set-Valued Volterra Integral Equations,” American J. Appl. Math. Stat., 1(3), 41-45, 2013. |
|
[20] | Naher, H., and Abdullah, F. A., “New traveling wave solutions by the extended generalized Riccati equation mapping method of the (2+1)-dimensional evolution equation,” J. Appl. Math. Article ID 486458, 18 pages, 2012. |
|
[21] | Wang, M., Li, X. and Zhang, J., “The (G’/G)-expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics,” Phys. Lett. A, 372, 417-423, 2008. |
|
[22] | Zayed, E.M.E. and Al-Joudi, S., “Applications of an extended (G’/G)-Expansion Method to Find Exact Solutions of Nonlinear PDEs in Mathematical Physics,” Math. Prob. Eng., Article ID 768573, 19 pages, 2010. |
|
[23] | Ozis, T. and Aslan, I., “Application of the (G’/G)-expansion method to Kawahara type equations using symbolic computation,” Appl. Math. Computation, 216, 2360-2365, 2010. |
|
[24] | Naher, H., Abdullah, F.A. and Akbar, M.A., “The (G’/G)-expansion method for abundant traveling wave solutions of Caudrey-Dodd-Gibbon equation,” Math. Prob. Eng., Article ID: 218216, 11 pages, 2011. |
|
[25] | Jabbari, A., Kheiri, H. and Bekir, A., “Exact solutions of the coupled Higgs equation and the Miccari system using He’s semi-inverse method and (G’/G)-expansion method,” Computers Math. Appli., 62, 2177-2186, 2011. |
|
[26] | Naher, H. and Abdullah, F.A., “The basic (G’/G)-expansion method for the fourth order Boussinesq equation,” Appl. Math., 3, 1144-1152, 2012. |
|
[27] | Zhang, J. Jiang, F. and Zhao, X., “An improved (G’/G)-expansion method for solving nonlinear evolution equations,” Int. J. Computer Math., 87, 1716-1725, 2010. |
|
[28] | Zhao, Y.M., Yang, Y.J. and Li, W., “Application of the improved (G’/G)-expansion method for the Variant Boussinesq equations,” Appl. Math. Sci., 5, 2855-2861, 2011. |
|
[29] | Nofel, T.A, Sayed, M., Hamad, Y.S. and Elagan, S.K., “The improved (G’/G)-expansion method for solving the fifth-order KdV equation,” Annals of Fuzzy Math. Informatics, 3, 9-17, 2011. |
|
[30] | Naher, H., Abdullah, F.A. and Akbar, M.A., “New traveling wave solutions of the higher dimensional nonlinear evolution equation by the improved (G’/G)-expansion method,” World Appl. Sci. J., 16, 11-21, 2012. |
|
[31] | Naher, H. and Abdullah, F.A., “Some new traveling wave solutions of the nonlinear reaction diffusion equation by using the improved (G’/G)-expansion method,” Math. Prob. Eng., Article ID: 871724, 17 pages, 2012. |
|
[32] | Naher, H. and Abdullah, F.A., “The improved (G’/G)-expansion method for the (2+1)-dimensional modified Zakharov-Kuznetsov equation,” J. Appl. Math., Article ID: 438928, 20 pages, 2012. |
|
[33] | Naher, H., Abdullah, F.A. and Bekir, A., “Abundant traveling wave solutions of the compound KdV-Burgers equation via the improved (G’/G)-expansion method,” AIP Advances, 2, 042163; 2012. |
|
[34] | Peng, Y.Z. and Krishnan, E.V., “Exact travelling wave solutions to the (3+1)-dimensional Kadomtsev-Petviashvili equation,” Acta, Physica Polonica, 108, 421-428, 2005. |
|
[35] | Khalfallah, M., “New exact traveling wave solutions of the (3+1)-dimensional Kadomtsev-Petviashvili equation,” Commun. Nonlinear Sci. Numer. Simul., 14, 1169-1179, 2009. |
|
[36] | Bekir, A. and Uygun, F., “Exact travelling wave solutions of nonlinear evolution equations by using the (G’/G)-expansion method,” Arab J. Math. Sci., 18, 73-85, 2012. |
|