Wronskian Determinant Solutions for the (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation

Abstract

In this paper, we consider (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation. Based on the bilinear form, we derive exact solutions of (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation by using the Wronskian technique, which include rational solutions, soliton solutions, positons and negatons.

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Ma, H. and Bai, Y. (2013) Wronskian Determinant Solutions for the (3 + 1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation. Journal of Applied Mathematics and Physics, 1, 18-24. doi: 10.4236/jamp.2013.15004.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] N. C. Freeman and J. J. C. Nimmo, “Soliton Solutions of the Korteweg-de Vries and Kadomtsev-Petviashvili Equations: The Wronskian Technique,” Physics Letters A, Vol. 95, No. 1, 1983, pp. 1-3.
http://dx.doi.org/10.1016/0375-9601(83)90764-8
[2] M. Boiti, J. J.-P. Leon and F. Pempinelli, “On the Spectral Transform of a Korteweg-de Vries Equation in Two Spatial Dimensions,” Inverse Problems, Vol. 2, No. 3, 1986, pp. 271-279.
http://dx.doi.org/10.1088/0266-5611/2/3/005
[3] C.-J. Bai and H. Zhao, “New Solitary Wave and Jacobi Periodic Wave Excitations in (2+1)-Dimensional Boiti-Leon-Manna-Pempinelli System,” International Journal of Modern Physics B, Vol. 22, No. 15, 2008, pp. 2407-2420. http://dx.doi.org/10.1142/S021797920803954X
[4] Y. Li and D. Li, “New Exact Solutions for the (2+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation,” Applied Mathematical Sciences, Vol. 6, No. 12, 2012, pp. 579-587.
[5] L. Luo, “New Exact Solutions and B?cklund Transformation for Boiti-Leon-Manna-Pempinelli Equation,” Physics Letters A, Vol. 375, No. 7, 2011, pp. 1059-1063.
http://dx.doi.org/10.1016/j.physleta.2011.01.009
[6] L. Delisle and M. Mosaddeghi, “Classical and SUSY Solutions of the Boiti-Leon-Manna-Pempinelli Equation,” Journal of Physics A: Mathematical and Theoretical, Vol. 46, No. 11, 2013, Article ID: 115203.
http://dx.doi.org/10.1088/1751-8113/46/11/115203
[7] M. Najafi and S. Arbabi, “Wronskian Determinant Solutions of the (2+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equation,” International Journal of Advanced Mathematical Sciences, Vol. 1, No. 1, 2013, pp. 8-11.
[8] M. Darvishi, M. Najafi, L. Kavitha and M. Venkatesh, “Stair and Step Soliton Solutions of the Integrable (2+1) and (3+1)-Dimensional Boiti-Leon-Manna-Pempinelli Equations,” Communications in Theoretical Physics, Vol. 58, No. 6, 2012, pp. 785-794.
http://dx.doi.org/10.1088/0253-6102/58/6/01
[9] R. Hirota, “The Direct Method in Soliton Theory,” Cambridge University Press, Cambridge, 2004.
[10] W. X. Ma, “Wronskians, Generalized Wronskians and Solutions to the Korteweg-de Vries Equation,” Chaos, Solitons and Fractals, Vol. 19, No. 1, 2004, pp. 163-170.
http://dx.doi.org/10.1016/S0960-0779(03)00087-0
[11] W.-X. Ma and Y. You, “Solving the Korteweg-de Vries Equation by Its Bilinear Form: Wronskian Solutions,” Transactions of the American Mathematical Society, Vol. 357, No. 5, 2005, pp. 1753-1778.
http://dx.doi.org/10.1090/S0002-9947-04-03726-2
[12] C.-X. Li, W.-X. Ma, X.-J. Liu and Y.-B. Zeng, “Wronskian Solutions of the Boussinesq Equation—Solitons, Negatons, Positons and Complexitons,” Inverse Problems, Vol. 23, No. 1, 2007, pp. 279-296.
http://dx.doi.org/10.1088/0266-5611/23/1/015

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