JAMP  Vol.2 No.7 , June 2014
The Modified Kadomtsev-Petviashvili Equation with Binary Bell Polynomials
Abstract: 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.
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.