Integrability in differential coverings

Abstract

Let $\tau :\tilde{\mathcal{E}}\to \mathcal{E}$ be a differential covering of a PDE $\tilde{\mathcal{E}}$ over $\mathcal{E}$. We prove that if $\mathcal{E}$ possesses infinite number of symmetries and/or conservation laws then $\tilde{\mathcal{E}}$ has similar properties.

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