Integrability properties of symmetric 4+4-dimensional heavenly type equation

L. V. Bogdanov; B. G. Konopelchenko

doi:10.1088/1751-8121/ab2f5e

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arXiv · 1905.00887

Integrability properties of symmetric 4+4-dimensional heavenly type equation

L. V. Bogdanov·B. G. Konopelchenko

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Abstract

We demonstrate that the dispersionless $\bar\partial$-dressing method developed before for general heavenly equation is applicable to the $4+4$ and $2N+2N$ - dimensional symmetric heavenly type equations. We introduce generating relation and derive the two-form defining the potential and equation for it. We develop the dressing scheme, calculate a class of special solutions and demonstrate that reduction from $4+4$-dimensional equation to four-dimensional general heavenly equation can be effectively performed on the level of the dressing data. We consider also the extension of the proposed scheme to $2N+2N$-dimensional case.

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L. V. Bogdanov, B. G. Konopelchenko. 2019-05-02. Integrability properties of symmetric 4+4-dimensional heavenly type equation. https://doi.org/10.1088/1751-8121%2Fab2f5e

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