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Ablowitz, M.J. and Segur, H. (1981) Solitions and Inverse Scattering Transform. SIAM, Philadelphia. http://dx.doi.org/10.1137/1.9781611970883
Malfliet, W. (1992) Solitary Wave Solutions of Nonlinear Wave Equation. American Journal of Physics, 60, 650-654. http://dx.doi.org/10.1119/1.17120
Malfliet, W. and Hereman, W. (1996) The Tanh Method: Exact Solutions of Nonlinear Evolution and Wave Equations. Physica Scripta, 54, 563-568. http://dx.doi.org/10.1119/1.17120
Wazwaz, A.M. (2004) The Tanh Method for Travelling Wave Solutions of Nonlinear Equations. Applied Mathematics and Computation, 154, 714-723. http://dx.doi.org/10.1016/S0096-3003(03)00745-8
EL-Wakil, S.A. and Abdou, M.A. (2007) New Exact Travelling Wave Solutions Using Modified Extented Tanh-Function Method. Chaos, Solitons & Fractals, 31, 840-852. http://dx.doi.org/10.1016/j.chaos.2005.10.032
Fan, E. (2000) Extended Tanh-Function Method and Its Applications to Nonlinear Equations. Physics Letters A, 277, 212-218. http://dx.doi.org/10.1016/S0375-9601(00)00725-8
Abdelrahman, M.A.E., Zahran, E.H.M. and Khater, M.M.A. (2015) Exact Traveling Wave Solutions for Modified Liouville Equation Arising in Mathematical Physics and Biology. International Journal of Computer Applications, 112.
Wazwaz, A.M. (2005) Exact Solutions to the Double Sinh-Gordon equation by the Tanh Method and a Variable Separated ODE. Computational Methods in Applied Mathematics, 50, 1685-1696. http://dx.doi.org/10.1016/j.camwa.2005.05.010
Wazwaz, A.M. (2004) A Sine-Cosine Method for Handling Nonlinear Wave Equations. Mathematical and Computer Modelling, 40, 499-508. http://dx.doi.org/10.1016/j.mcm.2003.12.010
Yan, C. (1996) A Simple Transformation for Nonlinear Waves. Physics Letters A, 224, 77-84. http://dx.doi.org/10.1016/S0375-9601(96)00770-0
Fan, E. and Zhang, H. (1998) A Note on the Homogeneous Balance Method. Physics Letters A, 246, 403-406. http://dx.doi.org/10.1016/S0375-9601(98)00547-7
Abdelrahman, M.A.E., Zahran, E.H.M. and Khater, M.M.A. (2014) Exact Traveling Wave Solutions for Power Law and Kerr Law Non Linearity Using the Exp -Expansion Method. Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, 14, 52-60.
Abdelrahman, M.A.E. and Khater, M.M.A. (2015) The -Expansion Method and Its Application for Solving Nonlinear Evolution Equations. International Journal of Science and Research, 4, 2319-7064.
Fan, E. and Zhang, J. (2002) Applications of the Jacobi Elliptic Function Method to Special-Type Nonlinear Equations. Physics Letters A, 305, 383-392. http://dx.doi.org/10.1016/S0375-9601(02)01516-5
Liu, S., Fu, Z., Liu, S. and Zhao, Q. (2001) Jacobi Elliptic Function Expansion Method and Periodic Wave Solutions of Nonlinear Wave Equations. Physics Letters A, 289, 69-74. http://dx.doi.org/10.1016/S0375-9601(01)00580-1
Zahran E.H.M. and Khater, M.M.A. (2014) Exact Traveling Wave Solutions for the System of Shallow Water Wave Equations and Modied Liouville Equation Using Extended Jacobian Elliptic Function Expansion Method. American Journal of Computational Mathematics, 4.
Abdou, M.A. (2007) The Extended F-Expansion Method and Its Application for a Class of Nonlinear Evolution Equations. Chaos, Solitons & Fractals, 31, 95-104. http://dx.doi.org/10.1016/j.chaos.2005.09.030
Ren, Y.J. and Zhang, H.Q. (2006) A Generalized F-Expansion Method to Find Abundant Families of Jacobi Elliptic Function Solutions of the (2 + 1)-Dimensional Nizhnik-Novikov-Veselov Equation. Chaos, Solitons & Fractals, 27, 959-979. http://dx.doi.org/10.1016/j.chaos.2005.04.063
Zhang, J.L., Wang, M.L., Wang, Y.M. and Fang, Z.D. (2006) The Improved F-Expansion Method and Its Applications. Physics Letters A, 350, 103-109. http://dx.doi.org/10.1016/j.physleta.2005.10.099
He, J.H. and Wu, X.H. (2006) Exp-Function Method for Nonlinear Wave Equations. Chaos, Solitons & Fractals, 27, 700-708. http://dx.doi.org/10.1016/j.chaos.2006.03.020
Aminikhad, H., Moosaei, H. and Hajipour, M. (2009) Exact Solutions for Nonlinear Partial Differential Equations via Exp-Function Method. Numerical Methods for Partial Differential Equations, 26, 1427-1433.
Zhang, Z.Y. (2008) New Exact Traveling Wave Solutions for the Nonlinear Klein-Gordon Equation. Turkish Journal of Physics, 32, 235-240.
Wang, M.L., Zhang, J.L. and Li, X.Z. (2008) The -Expansion Method and Travelling Wave Solutions of Nonlinear Evolutions Equations in Mathematical Physics. Physics Letters A, 372, 417-423. http://dx.doi.org/10.1016/j.physleta.2007.07.051
Zhang, S., Tong, J.L., Wang, W. (2008) A Generalized -Expansion Method for the mKdV Equation with Variable Coefficients. Physics Letters A, 372, 2254-2257. http://dx.doi.org/10.1016/j.physleta.2007.11.026
Zayed, E.M.E. and Gepreel, K.A. (2009) The -Expansion Method for Finding Traveling Wave Solutions of Nonlinear Partial Differential Equations in Mathematical Physics. Journal of Mathematical Physics, 50, 013502-013513. http://dx.doi.org/10.1063/1.3033750
Zahran, E.H.M. and Khater, M.M.A. (2014) Exact Solution to Some Nonlinear Evolution Equations by the -Expansion Method. Jokull Journal, 64.
Jawad, A.J.M., Petkovic, M.D. and Biswas, A. (2010) Modified Simple Equation Method for Nonlinear Evolution Equations. Applied Mathematics and Computation, 217, 869-877. http://dx.doi.org/10.1016/j.amc.2010.06.030
Zayed, E.M.E. (2011) A Note on the Modified Simple Equation Method Applied to Sharam-Tasso-Olver Equation. Applied Mathematics and Computation, 218, 3962-3964. http://dx.doi.org/10.1016/j.amc.2011.09.025
Zayed, E.M.E. and Hoda Ibrahim, S.A. (2012) Exact Solutions of Nonlinear Evolution Equation in Mathematical Physics Using the Modified Simple Equation Method. Chinese Physics Letters, 29, Article ID: 060201. http://dx.doi.org/10.1088/0256-307X/29/6/060201
Zayed, E.M.E. and Arnous, A.H. (2012) Exact Solutions of the Nonlinear ZK-MEW and the Potential YTSF Equations Using the Modified Simple Equation Method. AIP Conference Proceedings, 1479, 2044-2048. http://dx.doi.org/10.1063/1.4756591
Zayed, E.M.E. and Hoda Ibrahim, S.A. (2013) Modified Simple Equation Method and Its Applications for Some Nonlinear Evolution Equations in Mathematical Physics. International Journal of Computer Applications, 67, 39-44.
Zahran, E.H.M. and Khater, M.M.A. (2014) The Modified Simple Equation Method and Its Applications for Solving Some Nonlinear Evolutions Equations in Mathematical Physics. Jökull Journal, 64.
Petrovskii, S.V., Malchow, H. and Li, B.L. (2005) An Exact Solution of a Diffusive Predator-Prey System. Proceedings of the Royal Society A, 461, 1029-1053.
Wazwaz, A-M. (2005) The Tanh Method for Generalized Forms of Nonlinear Heat Conduction and Burgers-Fisher Equations. Applied Mathematics and Computation, 169, 321-338.
Ludwig, D., Jones, D.D. and Holling, C.S. (1978) Qualitative Analysis of Insect Outbreak Systems: The Spruce Budworm and Forest. Journal of Animal Ecology, 47, 315-332. http://dx.doi.org/10.2307/3939
Kraenkel, R.A., Manikandan, K. and Senthivelan, M. (2013) On Certain New Exact Colutions of a Diffusive Predator-Prey System. Communications in Nonlinear Science and Numerical Simulation, 18, 1269-1274. http://dx.doi.org/10.1016/j.cnsns.2012.09.019
Dehghan, M. and Sabouri, M. (2013) A Legendre Spectral Element Method on a Large Spatial Domain to Solve the Predator-Prey System Modeling Interaction Populations. Applied Mathematical Modeling, 37, 1028-1038. http://dx.doi.org/10.1016/j.apm.2012.03.030
Kudryasho, N. and Pickering, A. (1998) Rational Solutions for Schwarzian Integrable Hierarchies. Journal of Physics A: Mathematical and General, 31, 9505-9518. http://dx.doi.org/10.1088/0305-4470/31/47/011
Clarkson, P.A., Gordoa, P.R. and Pickering, A. (1997) Multicomponent Equations Associated to Non-Isospectral Scattering Problems. Inverse Problems, 13, 1463-1476. http://dx.doi.org/10.1088/0266-5611/13/6/004
Estevez, P.G. and Prada, J. (2004) A Generalization of the Sine-Gordon Equation Dimensions. Journal of Nonlinear Mathematical Physics, 11, 168-179. http://dx.doi.org/10.2991/jnmp.2004.11.2.3
Kim, H. and Choi, J.H. Exact Solutions of a Diffusive Predator-Prey System by Generalized Riccati Equation. Bulletin of the Malaysian Mathematical Sciences Society.
Peng, Y. and Shen, M. (2006) On Exact Solutions of Bogoyavlenskii Equation. Pramana, 67, 449-456. http://dx.doi.org/10.1007/s12043-006-0005-1
Malik, A., Chand, F., Kumar, H. and Mishra, S.C. (2012) Exact Solutions of the Bogoyavlenskii Equation Using the Multiple -Expansion Method. Computers and Mathematics with Applications, 64, 2850-2859. http://dx.doi.org/10.1016/j.camwa.2012.04.018
Kumar, R., Kaushal, R.S. and Prasad, A. (2010) Solitary Wave Solutions of Selective Nonlinear Diffusion-Reaction Equations Using Homogeneous Balance Method. Indian Academy of Sciences, 75, 607-611.