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RETRACTED: The Modified Simple Equation Method and Its Applications in Mathematical Physics and Biology

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ABSTRACT

Short Retraction Notice

The paper does not meet the standards of "American Journal of Computational Mathematics".

This article has been retracted to straighten the academic record. In making this decision the Editorial Board follows COPE's Retraction Guidelines. The aim is to promote the circulation of scientific research by offering an ideal research publication platform with due consideration of internationally accepted standards on publication ethics. The Editorial Board would like to extend its sincere apologies for any inconvenience this retraction may have caused.

Editor guiding this retraction: Prof. Hari M. Srivastava (EiC of AJCM)

The full retraction notice in PDF is preceding the original paper, which is marked "RETRACTED".

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References

[1] Ablowitz, M.J. and Segur, H. (1981) Solitions and Inverse Scattering Transform. SIAM, Philadelphia.
http://dx.doi.org/10.1137/1.9781611970883
[2] 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
[3] 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
[4] 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
[5] 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
[6] 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
[7] 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.
[8] 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
[9] 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
[10] 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
[11] 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
[12] 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.
[13] 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.
[14] 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
[15] 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
[16] 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.
[17] 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
[18] 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
[19] 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
[20] 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
[21] 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.
[22] Zhang, Z.Y. (2008) New Exact Traveling Wave Solutions for the Nonlinear Klein-Gordon Equation. Turkish Journal of Physics, 32, 235-240.
[23] 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
[24] 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
[25] 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
[26] Zahran, E.H.M. and Khater, M.M.A. (2014) Exact Solution to Some Nonlinear Evolution Equations by the -Expansion Method. Jokull Journal, 64.
[27] 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
[28] 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
[29] 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
[30] 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
[31] 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.
[32] 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.
[33] 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.
[34] Bogoyavlenskii, O.I. (1990) Breaking Solitons in 2+1-Dimensional Integrable Equations. Russian Mathematical Surveys, 45, 1-86.
http://dx.doi.org/10.1070/RM1990v045n04ABEH002377
[35] 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.
[36] 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
[37] 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
[38] 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
[39] 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
[40] 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
[41] 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
[42] 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.
[43] 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
[44] 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
[45] 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.

  
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