Application of G'/G-expansion method to the (2+1)-dimensional dispersive long wave equation
Subject Areas : Numerical AnalysisJafar Biazar 1 , Zeinab Ayati 2
1 - Department of Mathematics, Faculty of Science, University of Guilan
2 - Department of Mathematics, Faculty of Science, University of Guilan
Keywords: G', /G-expansion method, (2+1)-dimensional dispersive long wave equation,
Abstract :
In this work G'/G-expansion method has been employed to solve (2+1)-dimensional dispersive long wave equation. It is shown that G'/G-expansion method, with the help of symbolic computation, provides a very effective and powerful mathematical tool, for solving this equation.
[1] A.M. Wazwaz, The tanh method: Exact solutions of the Sine–Gordon and Sinh– Gordon equations, Appl. Math. Comput. 167 (2005)1196–1210.
[2] Mal.iet W, Hereman W. The tanh method: I. Exact solutions of nonlinear evolution and wave equations. Phys Scr 1996; 54:563–8.
[3] Wazwaz AM. The tanh and the sine–cosine methods for a reliable treatment of the modified equal width equation and its variants.Commun Nonlinear Sci Numer Simul 2006; 11:148–60.
[4] J. Biazar, H. Ghazvini, Exact solutions for non-linear Schrödinger equations by He’s homotopy perturbation method Physics Letters A 366 (2007), 79-84.
[5] J.H. He, Application of homotopy perturbation method to nonlinear wave equations, Chaos Solitons Fractals 26(2005) 695–700.
[6] J.H. He, Variational iteration method—a kind of non-linear analytical technique: some examples, Int. J. Nonlinear Mech. 34 (1999) 699–708.
[7] J.H. He, Variational iteration method for autonomous ordinary differential systems, Appl. Math. Comput. 114 (2000) 115–123.
[8] J.Biazar, E. Babolian, A. Nouri, R. Islam, An alternate algorithm for computing Adomian Decomposition method in special cases, Applied Mathematics and Computation 38 (2-3) (2003) 523- 529.
[9] J.H. He, X.H. Wu, Exp-function method for nonlinear wave equations, Chaos Solitons Fractals 30 (2006) 700–708.
[10] S. Zhang, Application of Exp-function method to a KdV equation with variable coefficients, Phys. Lett. A 365(2007) 448–453.
[11] J. biazar, z. ayati, Application of Exp-function method to Equal-width wave equation, Physica Scripta (2008) 78 045005.
[12] M.L. Wang, Exact solutions for a compound KdV-Burgers equation, Phys. Lett. A 213 (1996) 279.
[13] M.A. Abdou, The extended F-expansion method and its application for a class of nonlinear evolution equations, Chaos Solitons Fractals 31 (2007) 95-104.
[14] M.L. Wang, X.Z. Li, J.L. Zhang, The expansion method and travelling wave solutions of nonlinear evolution equations in mathematical physics, phys. Lett. A 372 (2008) 417–423.
[15] Zhang S. A generalized _ expansion method for the mKdV equation with variable coef.cients. Phys Lett A 2008; 372(13):2254–7.
[16] M. Boiti, J.J.P. Leon, F. Pempinelli, Spectral transform for a two spatial dimension extension of the dispersive long wave equation, Inverse Probl. 3 (1987) 371–387.
[17] Paquin, G. and Winternitz, P., Group theoretical analysis of dispersive long wave equations equation in two space dimensions, Physica D, 1990, 46: 122-138.
[18] Lou SY. Nonclassical symmetry reductions for the dispersive wave equations in shallow water. J Math Phys1992; 33:4300–5.
[19] Lou, S. Y., Similarity solutions of dispersive long wave equations in two space dimensions, Math. Meth. Appl. Sci., 1995, 18: 789-802.
[20] Lou, S. Y., Symmetries and algebras of the integrable dispersive long wave equations in (2+1)- dimensional spaces, J. Phys. A, 1994, 27: 3235-3243.
[21] Zhang, J. F., BBlund transformation and multisoliton-like solution of the (2+1)-dimensional dispersive long wave equations, Commun. Theor. Phys., 2000, 33: 577-582.
[22] C. Kong, D. Wang, L. Song, H. Zhang, New exact solutions to MKDV-Burgers equation and (2 + 1)-dimensional dispersive long wave equation via extended Riccati equation method, Chaos Solitons and Fractals xxx (2007) xxx–xxx.