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For a systemY of partial differential equations, the notion of a coveringŶ
∞ is introduced whereY
∞ is infinite prolongation ofY. Then nonlocal symmetries ofY are defined as transformations ofŶ
∞ which conserve the underlying contact structure. It turns out that generating functions of...
We consider an extension of Lawvere's Theorem showing that all classical results on limitations (i.e. Cantor, Russel, Godel, etc.) stem from the same underlying connection between self-referentiality and fixed points. We first prove an even stronger version of this result. Secondly, we...
Starting with Lie's classical theory, we carefully explain the basic notions of the higher symmetries theory for arbitrary systems of partial differential equations as well as the necessary calculation procedures. Roughly speaking, we explain what analogs of ‘higher KdV equations’ are for an...
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