Generalized Bäcklund transformation and new explicit solutions of the two-dimensional Toda equation. (English) Zbl 0930.35166
Clarkson, Peter A. (ed.) et al., Symmetries and integrability of difference equations. Proceedings of the 2nd international conference, Canterbury, UK, July 1–5, 1996. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 255, 15-22 (1999).
Summary: We obtain a generalized Bäcklund transformation for the bilinear representation of the two-dimensional Toda lattice equation, in which Bäcklund parameters are functions of \(x\), \(y\), \(n\). Furthermore, corresponding nonlinear superposition formulae are derived, and using these results, we obtain some new explicit solutions of the two-dimensional Toda lattice equation.
For the entire collection see [Zbl 0910.00045].
For the entire collection see [Zbl 0910.00045].
MSC:
| 35Q58 | Other completely integrable PDE (MSC2000) |
| 37K60 | Lattice dynamics; integrable lattice equations |
| 35R10 | Partial functional-differential equations |
| 37K35 | Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems |
