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Bell Polynomials to the Kadomtsev-Petviashivili Equation with Self-Consistent Sources

Published online by Cambridge University Press:  27 January 2016

Shufang Deng
Shufang Deng*
Affiliation:
Department of Mathematics, East China University of Science and Technology, Shanghai 200237, China
*
*Corresponding author. Email:sfangd@163.com (S. F Deng)
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Abstract

Bell Polynomials play an important role in the characterization of bilinear equation. Bell Polynomials are extended to construct the bilinear form, bilinear Bäckhand transformation and Lax pairs for the Kadomtsev-Petviashvili equation with self-consistent sources.

Keywords

Bell polynomialsbilinear formbilinear Backhand transformationLax pair
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 2 , April 2016 , pp. 271 - 278
Copyright
Copyright © Global-Science Press 2016 

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References

[1]Xiao, T. and Zeng, Y. B., Generalized Darboux transformation of the KP equation with self-consisitent sources, J. Phys. A Math. Gen. 37 (2004), pp. 7143–7162.CrossRefGoogle Scholar
[2]Zhang, D.J. and Chen, D. Y., The N-soliton solutions for the modified KdV equation with self-consistent sources, J. Phys. Soc. Japan, 71 (2002), pp. 2649–2656.Google Scholar
[3]Mel'nikov, V. K., A direct method for deriving a multi-soliton solution for the problem of interaction of waves on the x, y plane, Commun. Math. Phys., 112 (1987), pp. 639–552.CrossRefGoogle Scholar
[4]Mel'nikov, V. K., Integrable method of the KdV equation with a self-consisitent source, Phys. Lett. A, 133 (1988), pp. 493–496.Google Scholar
[5]Ma, W. X., Complexiton solutions of the Korteweg-de Vries equation with self-consistent sources, Chaos Soliton Fractals, 26 (2005), pp. 1453–1458.Google Scholar
[6]Hirota, R., Exact solutions of the Korteweg-de Vries equation for multiple collisions of solutions, Phys. Rev. Lett., 27 (1971), pp. 1192–1194.Google Scholar
[7]Hirota, R., A new form of Backlund transformation and its relation to the inverse scattering problem, Prog. Theor. Phys., 52 (1974), pp. 1498–1512.CrossRefGoogle Scholar
[8]Gilson, C., Lambert, F., Nimmo, J. and Willox, R., On the combinatorics of the Hirota D-operators, Proc. Soc. London A, 452 (1996), pp. 223–234.Google Scholar
[9]Lambert, F., Loris, I. and Springael, J., Classical Darboux transformations and the KP hierarchy, Inverse Problem, 17 (2001), pp. 1067–1074.Google Scholar
[10]Lambert, F. and Springael, J., Soliton equations and simple combinatorics, Acta Apll. Math., 102 (2008), pp. 147.Google Scholar
[11]Fan, E. G., The inregrability of nonisospectral and variable-coefficient KdV equation with binary Bell polynomials, Phy. Lett. A, 375 (2011), pp. 493–497.CrossRefGoogle Scholar
[12]Wang, Y. H. and Chen, Y., Binary Bell polynomials, bilinear approach to exact periodic wave solutions of (2+1)-dimensional nonlinear evolution equations, Commun. Theor. Phys., 56 (2011), pp.672–678.CrossRefGoogle Scholar
[13]Liu, N. and Liu, X. Q., Application of the binary Bell polynomials method to the dissipative (2+1)- dimensional AKNS equation, Chin. Phys. Lett., 29 (2012), 120201.Google Scholar
[14]Ma, W. X., Bilinear equations and resonant solutions and characterized by Bell polynomials, Reports Math. Phys., 72 (2013), pp. 41–56.Google Scholar