Symmetries of PDE systems and correspondences between jet spaces (Q631826)

For a smooth manifold \(M\) let \(J^k_mM\) be the space of \(k\)-jets of \(m\)-dimensional (locally closed) submanifolds of \(M\). A system of PDEs is considered as \({\mathcal R}\subseteq J^k_mM\). We can associate with \({\mathcal R}\) another system \({\mathcal R}^*\subseteq T^*M\) with only one unknown function. The present paper deals with the very interesting relationship between different types of symmetries of \({\mathcal R}\) and \({\mathcal R}^*\). One of the main tools is the theory of jet spaces in the Weil bundles framework.