Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations

M.T. Darvishi; M. Najafi; L. Kavitha; M. Venkatesh

PDF(4580 KB)

理论物理通讯 ›› 2012, Vol. 58 ›› Issue (06) : 785-794.

Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations

作者信息 +

Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations

Author information +

文章历史 +

摘要

The multiple exp-function method is a new approach to obtain multiple wave solutions of nonlinear partial differential equations (NLPDEs). By this method one can obtain multi-soliton solutions of NLPDEs. In this paper, using computer algebra systems, we apply the multiple exp-function method to construct the exact multiple wave solutions of a (2+1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Also, we extend the equation to a (3+1)-dimensional case and obtain some exact solutions for the new equation by applying the multiple exp-function method. By these applications, we obtain single-wave, double-wave and multi-wave solutions for these equations.

Abstract

导出引用

M.T. Darvishi, M. Najafi, L. Kavitha, 等. Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations[J]. 理论物理通讯, 2012, 58(06): 785-794

M.T. Darvishi, M. Najafi, L. Kavitha, et al. Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations[J]. Communications in Theoretical Physics, 2012, 58(06): 785-794

中图分类号： 02.30.Jr 02.70.Wz

参考文献

[1] A.V. Mikhailov, A.B. Shabat, and V.V. Sokolov, The Symmetry Approach to Classification of Integrable Equations. What is Integrability? Springer Ser. Nonlinear Dynam. Springer, Berlin (1991).
[2] A.V. Mikhailov and R.I. Yamilov, I. J. Phys. A 31 (1998) 6707.
[3] B.G. Konopelchenko, Introduction to Multidimensional Integrable Equations, Plenum, New York (1992).
[4] M. Boiti, J.P.P. Leon, L. Martina, and F. Pempinelli, Phys. Lett. A 132 (1988) 432.
[5] A. Fokas and P. Santini, Physica D 44 (1990) 99.
[6] J. Hietrarinta and R. Hirota, Phys. Lett. A 145 (1990) 237.
[7] K. Toda and S. Yu, J. Math. Phys. 41 (2000) 4747.
[8] M.T. Darvishi and F. Khani, Comput. Math. Appl. 58 (2009) 360.
[9] A. Aziz, F. Khani, and M.T. Darvishi, Zeitschrift f黵 Naturforschung A-Physical Sciences 65a (2010) 771.
[10] F. Khani, M.T. Darvishi, and R.S.R. Gorla, Comput. Math. Appl. 61 (2011) 1728.
[11] L. Kavitha, A. Prabhu, and D. Gopi, Chaos, Solitons and Fractals 42 (2009) 2322.
[12] L. Kavitha, N. Akila, A. Prabhu, O. Kuzmanovska-Barandovska, and D. Gopi, Math. Comput. Modelling 53 (2011) 1095.
[13] L. Kavitha, B. Srividya, and D. Gopi, J. Magn. Magn. Mater. 322 (2010) 1793.
[14] L. Kavitha, S. Jayanthi, A. Muniyappan, and D. Gopi, Phys. Scr. 84 (2011) 035803.
[15] L. Kavitha, P. Sathishkumar, and D. Gopi, Commun. Nonlinear Sci. Numer. Simulat. 15 (2010) 3900.
[16] L. Kavitha, P. Sathishkumar, and D. Gopi, Phys. Scr. 79 (2009) 015402(7pp).
[17] J.H. He and X.H. Wu, Chaos, Solitons and Fractals 30 (2006) 700.
[18] A. Ebaid, Phys. Lett. A 365 (2007) 213.
[19] B.C. Shin, M.T. Darvishi, and A. Barati, Comput. Math. Appl. 58 (2009) 2147.
[20] F. Khani, M.T. Darvishi, A. Farmani, and L. Kavitha, ANZIAM Journal 52 (2010) 110.
[21] M.T. Darvishi and F. Khani, Chin. Phys. Lett. 29(9) (2012) 09410.
[22] L. Kavitha, B. Srividya, and D. Gopi, Comput. Math. Appl. 62 (2011) 4691.
[23] Sirendaoreji, Phys. Lett. A 356 (2006) 124.
[24] Sirendaoreji, Chaos, Solitons and Fractals 19 (2004) 147.
[25] W.X. Ma and B. Fuchssteiner, Int. J. Non-Linear Mech. 31 (1996) 329.
[26] H.C. Ma, Y.D. Yu, and D.J. Ge, Appl. Math. Comput. 203 (2008) 792.
[27] Z.D. Dai, J. Liu, and D.L. Li, Appl. Math. Comput. 207 (2009) 360.
[28] C.J. Wang, Z.D. Dai, G. Mu, and S.Q. Lin, Commun. Theor. Phys. 52 (2009) 862.
[29] C.L. Zheng, J.Y. Qiang, and S.H. Wang, Commun. Theor. Phys. 54 (2010) 1054.
[30] Z.H. Zhao, Z.D. Dai, and S. Han, Appl. Math. Comput. 217 (2010) 4306.
[31] M.T. Darvishi and M. Najafi, Chin. Phys. Lett. 28 (2011) 040202.
[32] Mohammad Najafi, Maliheh Najafi, and M.T. Darvishi, Chin. Phys. Lett. 29 (2012) 040202.
[33] H.Z. Li, B. Tian, L.L. Li, and H.Q. Zhang, Commun. Theor. Phys. 53 (2010) 831.
[34] K.J. Cai, B. Tian, H. Zhang, and X.H. Meng, Commun. Theor. Phys. 52 (2009) 473.
[35] W.X. Ma, T. Huang, and Y. Zhang, Phys. Scr. 82 (2010) 065003.
[36] C.R. Gilson, J.J.C. Nimmo, and R. Willox, Phys. Lett. A 180 (1993) 337.
[37] L. Luo, Phys. Lett. A 375 (2011) 1059.
[38] L. Luo, Commun. Theor. Phys. 54 (2010) 208.
[39] S.H. Ma and J.P. Fang, Commun. Theor. Phys. 52 (2009) 641.
[40] G.T. Liu, Journal of Inner Mongolia Normal University (Natural Science Edition) 37 (2008) 145.
[41] N. Liu and X.Q. Liu, Chinese Journal of Quantum Electronics 25 (2008) 546 (in Chinese).
[42] L.L. Zhang, Journal of Liaocheng University (Nat. Sci.) 21 (2008) 35 (in Chinese).