Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-commutative lattice modified Gel'fand-Dikii systems   We introduce integrable multicomponent non-commutative lattice systems, which
can be considered as analogs of the modified Gel'fand-Dikii hierarchy. We
present the corresponding systems of Lax pairs and we show directly
multidimensional consistency of these Gel'fand-Dikii type equations. We
demonstrate how the systems can be obtained as periodic reductions of the
non-commutative lattice Kadomtsev-Petviashvilii hierarchy. The geometric
description of the hierarchy in terms of Desargues maps helps to derive
non-isospectral generalization of the non-commutative lattice modified
Gel'fand-Dikii systems. We show also how arbitrary functions of single
arguments appear naturally in our approach when making commutative reductions,
which we illustrate on the non-isospectral non-autonomous versions of the
lattice modified Korteweg-de Vries and Boussinesq systems.

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The categories of this paper are: funct-an
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The categories of this paper are: dg-ga
31
The categories of this paper are: ao-sci
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an