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In this paper we investigate the regularized long wave equation involving parameters by applying
the novel (G′/G)expansion method together with the generalized Riccati equation. The solutions obtained
in this manuscript may be imperative and significant for the explanation of some practical physical phenomena.
The performance of this method is reliable, useful, and gives us more new exact solutions than
the existing methods such as the basic (G′/G)expansion method, the extended (G′/G)expansion method,
the improved (G′/G)expansion method, the generalized and improved (G′/G)expansion method etc. The
obtained traveling wave solutions including solitons and periodic solutions are presented through the hyperbolic,
the trigonometric and the rational functions. The method turns out to be a powerful mathematical tool
and a step foward towards, albeit easily and yet efficiently, solving nonlinear evolution equations.
the novel (G′/G)expansion method together with the generalized Riccati equation. The solutions obtained
in this manuscript may be imperative and significant for the explanation of some practical physical phenomena.
The performance of this method is reliable, useful, and gives us more new exact solutions than
the existing methods such as the basic (G′/G)expansion method, the extended (G′/G)expansion method,
the improved (G′/G)expansion method, the generalized and improved (G′/G)expansion method etc. The
obtained traveling wave solutions including solitons and periodic solutions are presented through the hyperbolic,
the trigonometric and the rational functions. The method turns out to be a powerful mathematical tool
and a step foward towards, albeit easily and yet efficiently, solving nonlinear evolution equations.
Journal
Year
Volume
Issue
Physical description
Dates
received
11  7  2015
accepted
18  10  2015
online
7  12  2015
Contributors
author

Department of Mathematics, Pabna University of Science & Technology, Pabna6600,
Bangladesh
author
 Department of Mathematics, Faculty of Basic Education, PAAET, AlAardhiya, Kuwait
References
 [1] M. Wang, Solitary wave solutions for variant Boussinesq equations, Phy. Lett. A, 199 (1995) 169–172.
 [2] E.M.E. Zayed, H.A. Zedan and K.A. Gepreel, On the solitary wave solutions for nonlinear HirotaSasuma coupled KDV equations,Chaos, Solitons and Fractals, 22 (2004) 285–303.
 [3] L. Yang, J. Liu and K. Yang, Exact solutions of nonlinear PDE nonlinear transformations and reduction of nonlinear PDE to aquadrature, Phys. Lett. A 278 (2001) 267–270.
 [4] E.M.E. Zayed, H.A. Zedan and K.A. Gepreel, Group analysis and modified tanhfunction to find the invariant solutions andsoliton solution for nonlinear Euler equations, Int. J. Nonlinear Sci. Numer. Simul. 5 (2004) 221–234.[Crossref]
 [5] M. Inc and D.J. Evans, On traveling wave solutions of some nonlinear evolution equations, Int. J. Comput. Math. 8 (2004)191–202.[Crossref]
 [6] J.L. Hu, A new method of exact traveling wave solution for coupled nonlinear differential equations, Phys. Lett. A 322 (2004)211–216.
 [7] E.G. Fan, Extended tanhfunction method and its applications to nonlinear equations, Phys. Lett. A 277 (2000) 212218.
 [8] E.G. Fan, Multiple traveling wave solutions of nonlinear evolution equations using a unifiex algebraic method, J. Phys. A,Math. Gen. 35 (2002) 6853–6872.[Crossref]
 [9] Z.Y. Yan and H.Q. Zhang, New explicit and exact traveling wave solutions for a system of variant Boussinesq equations inmathematical physics, Phys. Lett. A 252 (1999) 291–296.
 [10] M.J. Ablowitz and P.A. Clarkson, Soliton, nonlinear evolution equations and inverse scattering, Cambridge University Press,New York, 1991.
 [11] M.G. Hafez, M.N. Alam and M.A. Akbar, Traveling wave solutions for some important coupled nonlinear physicalmodels via the coupled Higgs equation and the Maccari system, J. King Saud Univ.Sci. (2015) 27, 105–112. doi:10.1016/j.jksus.2014.09.001.[Crossref]
 [12] M.G. Hatez, M.N. Alam, and M.A. Akbar, Application of the exp(−ɸ(ɳ))expansion method to find exact solutions for thesolitary wave equation in an unmagnatized dusty plasma, World Applied Sciences Journal 32 (10): 21502155, 2014, DOI:10.5829/idosi.wasj.2014.32.10.3569.[Crossref]
 [13] H.O. Roshid, M.N. Alam, and M.A. Akbar, Traveling and Nontraveling Wave Solutions for Foam Drainage Equation, Int. J. ofAppl. Math and Mech., 10 (11): 65–75, 2014.
 [14] J.H. He and X.H. Wu, Expfunction method for nonlinear wave equations, Chaos, Solitons Fract. 30 (2006) 700–708.
 [15] S. Zhang, Application of Expfunction method to highdimensional nonlinear evolution equation, Chaos, Solitons Fract. 38(2008) 270–276.
 [16] M.L.Wang, X.Z. Li and J. Zhang, The (G′/G)expansion method and travelingwave solutions of nonlinear evolution equationsin mathematical physics, Phys. Lett. A, 372 (2008) 417–423.
 [17] M.N. Alam, M.A. Akbar and M.F. Hoque, Exact traveling wave solutions of the (3+1)dimensional mKdVZK equation and the(1+1)dimensional compound KdVB equation using new approach of the generalized (G′/G)expansion method, PramanaJournal of Physics, 83 (3) (2014) 317–329.[Crossref]
 [18] M.N. Alam and M.A. Akbar and H.O. Roshid, Traveling wave solutions of the Boussinesq equation via the new approach ofgeneralized (G′/G)Expansion Method, SpringerPlus, 3 (2014) 43 doi:10.1186/21931801343.[Crossref]
 [19] M.N. Alam and M.A. Akbar, Traveling wave solutions for the mKdV equation and the Gardner equation by new approach ofthe generalized (G′/G)expansion method, Journal of the Egyptian Mathematical Society, 22 (2014), 402–406.
 [20] E.M.E. Zayed and S. AlJoudi, Applications of an extended (G′/G)expansion method to find exact solutions of nonlinearPDEs in Mathematical Physics, Mathematical Problems in Engineering, Vol. 2010 Art. ID 768573 19 pages doi. 10.1155/2010/768573.
 [21] J. Zhang, F. Jiang and X. Zhao, An improved (G′/G)expansion method for solving nonlinear evolution equations, Int. J. Com.Math., 87(8) (2010) 1716–1725.
 [22] J. Zhang, X. Wei and Y. Lu, A generalized (G′/G)expansion method and its applications, Phys. Lett. A, 372 (2008) 3653–3658.
 [23] A. Bekir, Application of the (G′/G)expansion method for nonlinear evolution equations, Phys. Lett. A, 372 (2008) 3400–3406.
 [24] S. Zhang, J. Tong and W. Wang, A generalized (G′/G)expansion method for the mKdV equation with variable coeflcients,Phys. Lett. A, 372 (2008) 2254–2257.
 [25] M.A. Akbar, N.H.M. Ali and E.M.E. Zayed, A generalized and improved (G′/G)expansion method for nonlinear evolutionequations, Math. Prob. Engr., Vol. 2012 (2012), 22 pages. doi: 10.1155/2012/459879.[Crossref]
 [26] E.M.E. Zayed, New traveling wave solutions for higher dimensional nonlinear evolution equations using a generalized(G′/G)expansion method, J. Phys. A: Math. Theor., 42 (2009) 195202–195214.[Crossref]
 [27] M.M. Kabir, A. Borhanifar and R. Abazari, Application of (G′/G)expansion method to Regularized LongWave (RLW) equation,Computers and Mathematics with Applications 61(2011), 2044–2047.
 [28] R. Hirota, The direct method in soliton theory, Cambridge University Press, Cambridge, 2004.
 [29] J. Weiss, M. Tabor and G .Carnevale, The Painleve property for partial differential equations, J. Math. Phys. 24 (1983) 522.[Crossref]
 [30] M.N. Alam, M.A. Akbar and S.T. MohyudDin, A novel (G′/G)expansion method and its application to the Boussinesq equation,Chin. Phys. B, vol. 23(2), 2014, 020203020210, DOI: 10.1088/16741056/23/2/020203.[Crossref]
 [31] M. Shakeel and S.T. MohyudDin, New (G′/G)expansion method and its application to the ZKBBM equation, (2014). DOI:10.1016/j.jaubas.2014.02.007. (in press).[Crossref]
 [32] M.N. Alam and M.A. Akbar, Traveling wave solutions of the nonlinear (1+1)dimensional modified BenjaminBonaMahonyequation by using novel (G′/G)expansion method, Phys. Review Res. Int., 4(1) (2014) 147–165.
 [33] M.G. Hafez, M.N. Alam and M.A. Akbar, Exact traveling wave solutions to the KleinGordon equation using the novelexpansionmethod, Results in Physics 4 (2014) 177.
 [34] M. Shakeel, Q.M. UlHassan, and J. Ahmad, Applications of the novel (G′/G)expansion method for a time fractional simplifiedmodified MCH equation, Abstract Appl. Analysis, 2014 (2014) Article ID 601961 16 pages.
 [35] E. Eckstein, F.B.M. Belgacem, Model of platelet transport in flowing bloodwith drift and diffusion terms, Biophysical Journal,Vol.60, No.1, (1991) 53–69.[Crossref]
 [36] F.B.M. Belgacem, N. Smaoui, Interactions of Parabolic Convective Diffusion Equations and Navier Stokes Equations Connectedwith Population Dispersal, Communications on Applied Nonlinear Analysis, Vol. 8, No. 3, (2001) 47–67.
 [37] N. Smaoui, F.B.M. Belgacem, Connections between the Convective Diffusion Equation and the Forced Burgers Equation,Journal of Applied Mathematics and Stochastic Analysis, Vol. 15, No. 1, (2002) 57–75.
 [38] S. Zhu, The generalized Riccati equationmapping method in nonlinear evolution equation: application to (2+1)dimensionalBoitiLeonPempinelle equation. Chaos Soliton Fract. 37, (2008) 1335–1342.[Crossref]
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Publication order reference
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YADDA identifier
bwmeta1.element.psjddoi10_1515_wwfaa20150006