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arXiv · 0710.5543

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

Paolo Maria Santini·Adam Doliwa·Maciej Nieszporski
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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 $τ$ - function formulations and the Darboux-Bäcklund transformations of these novel dynamics.

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Paolo Maria Santini, Adam Doliwa, Maciej Nieszporski. 2007-10-29. Integrable dynamics of Toda-type on the square and triangular lattices. https://doi.org/10.1103/physreve.77.056601

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