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arXiv · 1701.02270

On a class of integrable systems of Monge-Amp\`ere type

Boris Doubrov·Eugene Ferapontov·Boris Kruglikov·Vladimir Novikov
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Abstract

We investigate a class of multi-dimensional two-component systems of Monge-Amp\`ere type that can be viewed as generalisations of heavenly-type equations appearing in self-dual Ricci-flat geometry. Based on the Jordan-Kronecker theory of skew-symmetric matrix pencils, a classification of normal forms of such systems is obtained. All two-component systems of Monge-Amp\`ere type turn out to be integrable, and can be represented as the commutativity conditions of parameter-dependent vector fields. Geometrically, systems of Monge-Amp\`ere type are associated with linear sections of the Grassmannians. This leads to an invariant differential-geometric characterisation of the Monge-Amp\`ere property.

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Boris Doubrov, Eugene Ferapontov, Boris Kruglikov, Vladimir Novikov. 2017-01-09. On a class of integrable systems of Monge-Amp\`ere type. https://doi.org/10.1063/1.4984982

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