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Some non-commutative integrable systems from Desargues maps

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Discrete Integrable Systems

We investigate periodic reductions of Desargues maps, which lead to novel integrable multicomponent lattice systems being non-commutative, non-isosectral, and non-autonomous analogues of the modified Gel’fand Dikii hierarchy. The equations are multidimensionally consistent, and we present the corresponding geometric systems of Lax pairs. We clarify the origin and appearance of functions of single variables, whose presence is indispensable in making further reductions to lattice Painlev equations.

This talk is part of the Isaac Newton Institute Seminar Series series.

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