  We assign some kind of invariant manifolds to a given integrable PDE (its
discrete or semi-discrete variant). First, we linearize the equation around its
arbitrary solution $u$. Then we construct a differential (respectively,
difference) equation compatible with the linearized equation for any choice of
$u$. This equation defines a surface called a generalized invariant manifold.
In a sense, the manifold generalizes the symmetry, which is also a solution to
the linearized equation. In this paper, we concentrate on continuous and
discrete models of hyperbolic type. It is known that such kind equations have
two hierarchies of symmetries, corresponding to the characteristic directions.
We have shown that properly chosen generalized invariant manifold allows one to
construct recursion operators that generate these symmetries. It is surprising
that both recursion operators are related to different parametrizations of the
same invariant manifold. Therefore, knowing one of the recursion operators for
the hyperbolic type integrable equation (having no pseudo-constants) we can
immediately find the second one.
