Integrable dynamics of Toda-type on the square and triangular lattices

Abstract

In a recent paper we constructed an integrable generalization of the Toda law on the square lattice. In this paper we construct other examples of integrable dynamics of Toda-type on the square lattice, as well as on the triangular lattice, as nonlinear symmetries of the discrete Laplace equations on the square and triangular lattices. We also construct the $\tau$ - function formulations and the Darboux-Bäcklund transformations of these novel dynamics.

22 pages, 4 figures

References in corpus (3)

• Discrete Riemann Surfaces and the Ising model
• Integrable discrete Schrodinger equations and a characterization of Prym varieties by a pair of quadrisecants
• The B-quadrilateral lattice, its transformations and the algebro-geometric construction

Cited by in corpus (4)

• Desargues maps and their reductions
• Integrable maps from Galois differential algebras, Borel transforms and number sequences
• Darboux transformations for linear operators on two dimensional regular lattices
• Linear problems and Bäcklund transformations for the Hirota-Ohta system