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

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.

14 pages

References in corpus (3)

• Linearly degenerate hierarchies of quasiclassical SDYM type
• Six-dimensional heavenly equation. Dressing scheme and the hierarchy
• On an integrable multi-dimensionally consistent 2n+2n-dimensional heavenly-type equation