All Title Author
Keywords Abstract


The Modified Kadomtsev-Petviashvili Equation with Binary Bell Polynomials

DOI: 10.4236/jamp.2014.27065, PP. 587-592

Keywords: Binary Bell Polynomials, Bilinear Bäcklund Transformation, Lax Pair

Full-Text   Cite this paper   Add to My Lib

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.

References

[1]  Ablowitz, M.J. and Clarkson, P.A. (1991) Solitons, Non-linear Evolution Equations and Inverse Scattering Transform. Cambridge University Press, Cambridge. http://dx.doi.org/10.1017/CBO9780511623998
[2]  Hirota, R. (1971) Exact Solution of the Korteweg-de Vries Equation Formultip le Collisions of Colitons. Physical Review Letters, 27, 1192-1194. http://dx.doi.org/10.1103/PhysRevLett.27.1192
[3]  Matveev, V.B. and Salle, M.A. (1991) Darboux Transformations and Solitons. Springer, Berlin.
http://dx.doi.org/10.1007/978-3-662-00922-2
[4]  Fan, E.G. (2000) Extended Tank-Function Method and Its Applications to Nonlinear Equations. Physics Letters A, 277, 212-218. http://dx.doi.org/10.1016/S0375-9601(00)00725-8
[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.
http://dx.doi.org/10.1111/j.1467-9590.2009.00435.x
[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.
http://dx.doi.org/10.1103/PhysRevE.78.036607
[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.
http://dx.doi.org/10.1088/1751-8113/42/9/095206
[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. http://dx.doi.org/10.1143/PTP.52.1498
[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. http://dx.doi.org/10.1098/rspa.1996.0013
[10]  Lambert, F., Loris, I. and Springael, J. (2001) Classical Darboux Transformations and the KP Hierarchy. Inverse Problems, 17, 1067-1074. http://dx.doi.org/10.1088/0266-5611/17/4/333
[11]  Lambert, F. and Springael, J. (2008) Soliton Equations and Simple Combinatorics. Acta Applicandae Mathematicae, 102, 147-178. http://dx.doi.org/10.1007/s10440-008-9209-3
[12]  Fan, E.G. (2011) The Integrability of Nonisospectral and Variable-coefficient KdV Equation with Binary Bell Polynomials. Physics Letters A, 375, 493-497.

Full-Text

comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

微信:OALib Journal