New Periodic and Soliton Solutions of (2 + 1)-Dimensional Soliton Equation
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Abstract
By using the sine-cosine method proposed recently, we give the exact periodic and soliton solutions of the (2 + 1)-dimensional soliton equation in this paper. Many new families of exact traveling wave solutions of the (2 + 1)-dimensional soliton equation are successfully obtained. The computation for the method appears to be easier and faster by generalmathematical software.
References
[1] A.M. Wazwaz, The tanh method: solitons and periodic solutions for the Dodd-Bullough-Tzikhailov and the Tzitzeica-Dodd-Bullough equations, Chaos, Solitons and Fractals 25 (2005) 55-63.
[2] A.M. Wazwaz, ”The tanh method and the sine-cosine method for solving the KP-MEW equation”, Int. J. Comput. Math., Vol.82, No.2, (2005), pp.235-246.
[3] A.M. Wazwaz, ”The tanh method for travelling wave solutions of nonlinear equations”, Appl. Math. Comput., Vol.154, No.3, (2004), pp.713-723.
[4] A.M. Wazwaz, ”The extended tanh method for new solitons solutions for many forms of the fifth-order KdV equations”, Appl. Math. Comput., Vol.184, No.2, (2007), pp.1002-1014. 238 S. Arbabi, M. Najafi, M. Najafi
[5] A.M. Wazwaz, The extended tanh method for abundant solitary wave solutions of nonlinear wave equations, Appl. Math. Comput 187 (2007), 1131-1142.
View more references (22)
[6] A.M. Wazwaz, ”New solitons and kinks solutions to the Sharma-TassoOlver equation”, Appl. Math. Comput., Vol.188, No.2, (2007), pp.1205-1213.
[7] E. Yusufo˜glu, A. Bekir, ”Solitons and periodic solutions of coupled nonlinear evolution equations by using sine-cosine method”, Int. J. Comput. Math., Vol.83, No.12, (2006), pp.915-924.
[8] F. Ta¸scan, A. Bekir, Analytic solutions of the (2 + 1)-dimensional nonlinear evolution equations using the sine-cosine method, Appl. Math. Comput 215 (2009), 3134-3139.
[9] S. Arbabi Mohammad-Abadi, ”Analytic solutions of the KadomtsevPetviashvili equation with power law nonlinearity using the sine-cosine method”, American Journal of Computational and Applied Mathematics., Vol.1, No.1, (2011), pp.1-4.
[10] Z. Xiqiang, W. Limin, S. Weijun, ”The repeated homogeneous balance method and its applications to nonlinear partial differential equations”, Chaos, Solitons and Fractals , Vol.28, No.2, (2006), 448-453.
[11] S.J. Liao, On the homotopy analysis method for nonlinear problems, Appl. Math. Comput 147 (2004), 499-513.
[12] S.J. Liao, A new branch of solutions of boundary-layer flows over an impermeable stretched plate, Int. J. Heat Mass Transfer 48 (2005), 2529-2539.
[13] M.T. Darvishi, F. Khani, A series solution of the foam drainage equation, Comput. Math. Appl 58 (2009), 360-368.
[14] F. Khani, M.T. Darvishi, R.S.R. Gorla, ” Analytical investigation for cooling turbine disks with a non-Newtonian viscoelastic fluid”, Appl. Math. Comput., Vol.61, No.7, (2011), pp.1728-1738.
[15] E. Fan, Z. Jian, ” Applications of the Jacobi elliptic function method to special-type nonlinear equations”, Phys. Lett. A., Vol.305, No.6, (2002), pp.383-392.
[16] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, ” Exact three-wave solutions for high nonlinear form of Benjamin-Bona-Mahony-Burgers equations”, International Journal of Computational and Mathematical Sciences., Vol.6, No.3, (2010), pp.127-131. New Periodic and Soliton solutions of (2 + 1)-dimensional soliton equation 239
[17] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, ” New exact solutions for the (3+1)-dimensional breaking soliton equation”, International Journal of Computational and Mathematical Sciences., Vol.6, No.2, (2010), pp.134-137.
[18] S.Arbabi Mohammad-Abadi, Maliheh Najafi , Extend three-wave method for the (3+1)-Dimensional Soliton Equation, World Academy of Science, Engineer-ing and Technology, 80 (2011), 1342-1345.
[19] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi, ”New application of EHTA for the generalized (2+1)-dimensional nonlinear evolution equations”, International Journal of Computational and Mathematical Sciences., Vol.6, No.3, (2010), pp.132-138.
[20] M.T. Darvishi, Mohammad Najafi, ”Some complexiton type solutions of the (3+1)-dimensional Jimbo-Miwa equations”, International Journal of Computational and Mathematical Sciences., Vol.6, No.1, (2012), pp.25-27.
[21] M.T. Darvishi, Maliheh Najafi, Mohammad Najafi , Traveling wave solutions for the (3+1)-dimensionalbreaking soliton equation by ( G′ G )- expansion method and modified F-expansion method, World Academy of Science, Engineer-ing and Technology, 88 (2012), 37-42.
[22] F. Khani, M.T. Darvishi, A. Farmani, L. Kavitha , New exact solutions of coupled (2+1)-dimensional nonlinear system of Schr¨odinger equations, ANZIAM Journal, 52 (2010), 110-121.
[23] X.H. Wu, J.H. He, ”Exp-function method and its application to nonlinear equations”, Chaos, Solitons and Fractals., Vol.38, No.3, (2008), pp.903-910.
[24] A. R. Adem, C. M. Khalique, A. Biswas , Solutions of KadomtsevPetviashvili equation with power law nonlinearity in 1+3 dimensions, Math. Meth. Appl. Sci, 34 (2011), 532-543.
[25] C. Ye, W. Zhang, New explicit solutions for (2 + 1)-dimensional soliton equation, Chaos Solitons Fractals 44 (2011) 1063-1069.
[26] K. Porsezian, Painlev analysis of new higher-dimensional soliton equation, J Math Phys 38 (1997) 4675-4679.
[27] Z. Y. Yan, Extended Jacobian elliptic function algorithm with symbolic computation to construct new doubly-periodic solutions of nonlinear differential equations, Comput. Phys. Commun. 148 (2002) 30-42