论文信息 - Rational solutions of a differential-difference KdV equation, the Toda equation and the discrete KdV equation

Rational solutions of a differential-difference KdV equation, the Toda equation and the discrete KdV equation

In this paper, a series of rational solutions are presented for a differential-difference analogue of the KdV equation, the Toda equation and the discrete KdV equation. These rational solutions are obtained using Hirota's bilinear formalism and Backlund transformations. The crucial step is the use of nonlinear superposition formulae.

P. Clarkson | Xing-Bao Hu

[1] J. Satsuma,et al. Bilinear discrete Painleve-II and its particular solutions , 1994, solv-int/9412007.

[2] Y. Ohta,et al. Bilinear Structure and Exact Solutions of the Discrete Painlev\'e I Equation , 1994 .

[3] P. Clarkson,et al. New exact solutions of the discrete fourth Painleve´equation , 1994, solv-int/9409002.

[4] Xing-Biao Hu. Nonlinear superposition formulae for the differential-difference analogue of the KdV equation and two-dimensional Toda equation , 1994 .

[5] Y. Ohta,et al. Casorati determinant solutions for the discrete Painlevé III equation , 1993, solv-int/9310002.

[6] K. M. Tamizhmani,et al. Schlesinger transforms for the discrete painlevé IV equation , 1993 .

[7] Ramani,et al. Discrete versions of the Painlevé equations. , 1991, Physical review letters.

[8] P. Clarkson,et al. Solitons, Nonlinear Evolution Equations and Inverse Scattering: References , 1991 .

[9] M. Kruskal,et al. New similarity reductions of the Boussinesq equation , 1989 .

[10] Ryogo Hirota,et al. A Simple Structure of Superposition Formula of the Bäcklund Transformation , 1978 .

[11] Ryogo Hirota,et al. Nonlinear Partial Difference Equations. : I. A Difference Analogue of the Korteweg-de Vries Equation , 1977 .

[12] Ryogo Hirota,et al. A Variety of Nonlinear Network Equations Generated from the Bäcklund Transformation for the Toda Lattice , 1976 .

[13] Morikazu Toda,et al. Studies of a non-linear lattice , 1975 .