The Tangent Covering

The tangent covering is an equation naturally related to the initial equation \(\mathbb {E}\) and which covers the latter and plays the same role in the category of differential equations that the tangent bundle plays in the category of smooth manifolds. It is used to construct recursion operators for symmetries of \(\mathbb {E}\) and symplectic structures on \(\mathbb {E}\). In this chapter we give the solution to Problem 1.18 and also prepare a basis to solution of Problems 1.20 (Chap. 7) and 1.22 (Chap. 8).