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arXiv · 1310.0203

Projective differential geometry of multidimensional dispersionless integrable hierarchies

L. V. Bogdanov·B. G. Konopelchenko
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Abstract

We introduce a general setting for multidimensional dispersionless integrable hierarchy in terms of differential $m$-form $\Omega_m$ with the coefficients satisfying the Pl\"ucker relations, which is gauge-invariantly closed and its gauge-invariant coordinates (ratios of coefficients) are (locally) holomorphic with respect to one of the variables (the spectral variable). We demonstrate that this form defines a hierarchy of dispersionless integrable equations in terms of commuting vector fields locally holomorphic in the spectral variable. The equations of the hierarchy are given by the gauge-invariant closedness equations.

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L. V. Bogdanov, B. G. Konopelchenko. 2013-10-01. Projective differential geometry of multidimensional dispersionless integrable hierarchies. https://doi.org/10.1088/1742-6596/482/1/012005

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