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Noncommutative Integrable Systems of Hydrodynamic Type

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Abstract

On noncommutative spaces, integrable hierarchies of hydrodynamic type systems (1\(^{st}\)-order quasilinear PDE’s) do not, in general, exist. Nevertheless, an infinite-component hydrodynamic chain defined below is shown to be integrable. Its modified version is also constructed and it exhibits a new purely noncommutative phenomenon: the number of modified variables is either \(2\) or \(\infty\).

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  1. The University of Tennessee Space Institute, Tullahoma, TN, 37388, USA

    Boris A. Kupershmidt

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  1. Boris A. Kupershmidt
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Correspondence to Boris A. Kupershmidt.

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Kupershmidt, B.A. Noncommutative Integrable Systems of Hydrodynamic Type. Acta Appl Math 92, 269–292 (2006). https://doi.org/10.1007/s10440-006-9054-1

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  • DOI: https://doi.org/10.1007/s10440-006-9054-1

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