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

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

2007-10-29

arxiv.org/abs/0710.5543v1

Phys. Rev. E 77 (2008) 056601

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages, 4 figures

Scientific paper

10.1103/PhysRevE.77.056601

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-B\"acklund transformations of these novel dynamics.

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