Seminar talk, 8 February 2017

From Geometry of Differential Equations
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Speaker: Vladimir Chetverikov

Title: Coverings from differential equations and C-invariant distributions

Coverings over a differential equations are used to compute its nonlocal symmetries and recursion operators. This talk discusses a simpler problem of constructing coverings from given equation and describing of covered equations. A natural approach to this problem is to describe the distribution defined by the fibers of the covering. We will show that this distribution is invariant with respect to the Cartan distribution (C-invariant) and integrable in infinite dimensional sense. Conversely, any integrable C-invariant distribution on infinitely prolonged equation gives a covering from this equation. The vertical component of the column of vector fields that define a C-invariant distribution is a matrix analog of evolution derivation, with the corresponding generating matrix satisfying a matrix analog of linearization equation.