On the symmetry classification of integrable chains in 3D. Darboux-integrable reductions and their higher symmetries

2025/12/30 by R. N. Garifullin, I. T. Habibullin · 1 voice · 1 citation
Physics and Astronomy · #nlin.SI

paper · pdf · doi:10.1088/1751-8121/ae4ba6

Abstract

This paper proposes a method for identifying and classifying integrable nonlinear equations with three independent variables, one of which is discrete and the other two are continuous. A characteristic property of this class of equations, called Toda-type chains, is that they admit finite-field reductions in the form of open chains with enhanced integrability. The paper results in a theorem stating that all known integrable Toda-type chains admit reductions in the form of an open chain of length three with a family of second-order evolutionary type symmetries. Apparently, this property of Toda-type chains can be used as an effective classification criterion when compiling lists of integrable differential-difference equations in 3D.

Citations

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Cited by

• Discrete integrable equations with three independent variables

Discussions

• R. N. Garifullin, I. T. Habibullin: On the symmetry classification of integrable chains in 3D. Darboux-integrable reductions and their higher symmetries https://arxiv.org/abs/2512.23984 https://arxiv. [bsky, 0 points, 0 comments]

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• On integrable reductions of two-dimensional Toda-type lattices
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• Classification of evolutionary equations on the lattice. I. The general theory