Application of the Novel (G′/G)-Expansion Method to the Regularized Long Wave Equation
Md. Nur Alam; Fethi Bin Muhammad Belgacem
Waves, Wavelets and Fractals (2015)
- Volume: 1, Issue: 1
- ISSN: 2449-5557
Access Full Article
topAbstract
topHow to cite
topReferences
top- [1] M. Wang, Solitary wave solutions for variant Boussinesq equations, Phy. Lett. A, 199 (1995) 169–172. Zbl1020.35528
- [2] E.M.E. Zayed, H.A. Zedan and K.A. Gepreel, On the solitary wave solutions for nonlinear Hirota-Sasuma coupled KDV equations, Chaos, Solitons and Fractals, 22 (2004) 285–303. Zbl1069.35080
- [3] L. Yang, J. Liu and K. Yang, Exact solutions of nonlinear PDE nonlinear transformations and reduction of nonlinear PDE to a quadrature, Phys. Lett. A 278 (2001) 267–270. Zbl0972.35003
- [4] E.M.E. Zayed, H.A. Zedan and K.A. Gepreel, Group analysis and modified tanh-function to find the invariant solutions and soliton 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] Zbl1047.65091
- [6] J.L. Hu, A new method of exact traveling wave solution for coupled nonlinear differential equations, Phys. Lett. A 322 (2004) 211–216. Zbl1118.81366
- [7] E.G. Fan, Extended tanh-function method and its applications to nonlinear equations, Phys. Lett. A 277 (2000) 212-218. Zbl1167.35331
- [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] Zbl1039.35029
- [9] Z.Y. Yan and H.Q. Zhang, New explicit and exact traveling wave solutions for a system of variant Boussinesq equations in mathematical physics, Phys. Lett. A 252 (1999) 291–296. Zbl0938.35130
- [10] M.J. Ablowitz and P.A. Clarkson, Soliton, nonlinear evolution equations and inverse scattering, Cambridge University Press, New York, 1991. Zbl0762.35001
- [11] M.G. Hafez, M.N. Alam and M.A. Akbar, Traveling wave solutions for some important coupled nonlinear physical models 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 the solitary wave equation in an unmagnatized dusty plasma, World Applied Sciences Journal 32 (10): 2150-2155, 2014, DOI: 10.5829/idosi.wasj.2014.32.10.3569. [Crossref]
- [13] H.O. Roshid, M.N. Alam, and M.A. Akbar, Traveling and Non-traveling Wave Solutions for Foam Drainage Equation, Int. J. of Appl. Math and Mech., 10 (11): 65–75, 2014.
- [14] J.H. He and X.H. Wu, Exp-function method for nonlinear wave equations, Chaos, Solitons Fract. 30 (2006) 700–708. Zbl1141.35448
- [15] S. Zhang, Application of Exp-function method to high-dimensional nonlinear evolution equation, Chaos, Solitons Fract. 38 (2008) 270–276. Zbl1142.35593
- [16] M.L.Wang, X.Z. Li and J. Zhang, The (G′/G)-expansion method and travelingwave solutions of nonlinear evolution equations in mathematical physics, Phys. Lett. A, 372 (2008) 417–423. [WoS]
- [17] M.N. Alam, M.A. Akbar and M.F. Hoque, Exact traveling wave solutions of the (3+1)-dimensional mKdV-ZK equation and the (1+1)-dimensional compound KdVB equation using new approach of the generalized (G′/G)-expansion method, Pramana Journal of Physics, 83 (3) (2014) 317–329. [WoS][Crossref]
- [18] M.N. Alam and M.A. Akbar and H.O. Roshid, Traveling wave solutions of the Boussinesq equation via the new approach of generalized (G′/G)-Expansion Method, SpringerPlus, 3 (2014) 43 doi:10.1186/2193-1801-3-43. [Crossref][WoS]
- [19] M.N. Alam and M.A. Akbar, Traveling wave solutions for the mKdV equation and the Gardner equation by new approach of the generalized (G′/G)-expansion method, Journal of the Egyptian Mathematical Society, 22 (2014), 402–406. Zbl1304.35180
- [20] E.M.E. Zayed and S. Al-Joudi, Applications of an extended (G′/G)-expansion method to find exact solutions of nonlinear PDEs in Mathematical Physics, Mathematical Problems in Engineering, Vol. 2010 Art. ID 768573 19 pages doi. 10. 1155/2010/768573. Zbl1207.35262
- [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. [WoS] Zbl1197.65161
- [22] J. Zhang, X. Wei and Y. Lu, A generalized (G′/G)-expansion method and its applications, Phys. Lett. A, 372 (2008) 3653–3658. [WoS] Zbl1220.37070
- [23] A. Bekir, Application of the (G′/G)-expansion method for nonlinear evolution equations, Phys. Lett. A, 372 (2008) 3400– 3406. Zbl1228.35195
- [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. [WoS] Zbl1220.37072
- [25] M.A. Akbar, N.H.M. Ali and E.M.E. Zayed, A generalized and improved (G′/G)-expansion method for nonlinear evolution equations, Math. Prob. Engr., Vol. 2012 (2012), 22 pages. doi: 10.1155/2012/459879. [Crossref] Zbl1264.35078
- [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. [WoS][Crossref] Zbl1170.35310
- [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. Zbl1219.65143
- [28] R. Hirota, The direct method in soliton theory, Cambridge University Press, Cambridge, 2004. Zbl1099.35111
- [29] J. Weiss, M. Tabor and G .Carnevale, The Painleve property for partial differential equations, J. Math. Phys. 24 (1983) 522. [Crossref] Zbl0514.35083
- [30] M.N. Alam, M.A. Akbar and S.T. Mohyud-Din, A novel (G′/G)-expansion method and its application to the Boussinesq equation, Chin. Phys. B, vol. 23(2), 2014, 020203-020210, DOI: 10.1088/1674-1056/23/2/020203. [WoS][Crossref]
- [31] M. Shakeel and S.T. Mohyud-Din, New (G′/G)-expansion method and its application to the ZK-BBM 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 Benjamin-Bona-Mahony equation 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 Klein-Gordon equation using the novelexpansion method, Results in Physics 4 (2014) 177.
- [34] M. Shakeel, Q.M. Ul-Hassan, and J. Ahmad, Applications of the novel (G′/G)-expansion method for a time fractional simplified modified MCH equation, Abstract Appl. Analysis, 2014 (2014) Article ID 601961 16 pages. [WoS]
- [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 Connected with Population Dispersal, Communications on Applied Nonlinear Analysis, Vol. 8, No. 3, (2001) 47–67. Zbl0988.35071
- [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. Zbl1043.35008
- [38] S. Zhu, The generalized Riccati equationmapping method in non-linear evolution equation: application to (2+1)-dimensional Boiti-Leon-Pempinelle equation. Chaos Soliton Fract. 37, (2008) 1335–1342. [Crossref][WoS] Zbl1142.35597