We apply the technique based on twisted extensions of symmetry algebras to construct new nonlinear four-dimensional differential coverings for the hyper-CR equation of Einstein–Weyl structures and for the associated integrable hierarchy. We expose related multi-component three-dimensional covering. By the symmetry reduction of the hyper-CR equation of Einstein–Weyl structures we derive nonlinear three-dimensional differential covering for the Gibbons-Tsarev equation.

中文翻译：

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爱因斯坦-魏尔结构的超CR方程和吉本斯-特萨列夫方程的非线性非等谱微分覆盖

我们应用基于对称代数的扭曲扩展的技术来构造新的非线性四维微分覆盖层，用于爱因斯坦-魏尔结构的hyper-CR方程以及相关的可积层次。我们公开了相关的多分量三维覆盖。通过对Einstein-Weyl结构的超CR方程的对称性简化，我们得出了Gibbons-Tsarev方程的非线性三维差分覆盖。