Share This Article:

The Modified Kadomtsev-Petviashvili Equation with Binary Bell Polynomials

Abstract Full-Text HTML XML Download Download as PDF (Size:248KB) PP. 587-592
DOI: 10.4236/jamp.2014.27065    3,096 Downloads   3,994 Views   Citations


Binary Bell Polynomials play an important role in the characterization of bilinear equation. The bilinear form, bilinear B?cklund transformation and Lax pairs for the modified Kadomtsev-Petviashvili equation are derived from the Binary Bell Polynomials.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Hu, N. and Deng, S. (2014) The Modified Kadomtsev-Petviashvili Equation with Binary Bell Polynomials. Journal of Applied Mathematics and Physics, 2, 587-592. doi: 10.4236/jamp.2014.27065.


[1] Ablowitz, M.J. and Clarkson, P.A. (1991) Solitons, Non-linear Evolution Equations and Inverse Scattering Transform. Cambridge University Press, Cambridge.
[2] Hirota, R. (1971) Exact Solution of the Korteweg-de Vries Equation Formultip le Collisions of Colitons. Physical Review Letters, 27, 1192-1194.
[3] Matveev, V.B. and Salle, M.A. (1991) Darboux Transformations and Solitons. Springer, Berlin.
[4] Fan, E.G. (2000) Extended Tank-Function Method and Its Applications to Nonlinear Equations. Physics Letters A, 277, 212-218.
[5] Hu, X.B., Lou, S.Y. and Qian, X.M. (2009) Nonlocal Symmetries for Bilinear Equations and Their Applications. Studies in Applied Mathematics, 122, 305-324.
[6] Fan, E.G. and Hon, Y.C. (2008) Quasiperiodic Waves and Asymptotic Behavior for Bogoyvlenskii’s Breaking Soliton Equation in (2 + 1) Dimensions. Phyical Review E, 78, Article ID: 036607.
[7] Fan, E.G. (2009) Quasi-Periodic Waves and Wsymptotic Property for the Asymmetrical Nizhnik-Novikov-Veselov Equation. Journal of Physics A Mathematical and Theoretical, 42, Article ID: 095206.
[8] Hirota, R. (1974) A New Form of Backlund Transformations and Its Relation to the Inverse Scattering Problem. Progress of Theoretical Physics, 52, 1498-1512.
[9] Gilson, C., Lambert, F., Nimmo, J. and Willox, R. (1996) On the Combinatoricd of the Hirota D-Operators. Proceedings the Royal of Society A, 452, 223-234.
[10] Lambert, F., Loris, I. and Springael, J. (2001) Classical Darboux Transformations and the KP Hierarchy. Inverse Problems, 17, 1067-1074.
[11] Lambert, F. and Springael, J. (2008) Soliton Equations and Simple Combinatorics. Acta Applicandae Mathematicae, 102, 147-178.
[12] Fan, E.G. (2011) The Integrability of Nonisospectral and Variable-coefficient KdV Equation with Binary Bell Polynomials. Physics Letters A, 375, 493-497.

comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.