On a direct algorithm for constructing recursion operators and Lax pairs for integrable models
  We suggested an algorithm for searching the recursion operators for nonlinear
integrable equations. It was observed that the recursion operator $R$ can be
represented as a ratio of the form $R=L_1^{-1}L_2$ where the linear
differential operators $L_1$ and $L_2$ are chosen in such a way that the
ordinary differential equation $(L_2-\lambda L_1)U=0$ is consistent with the
linearization of the given nonlinear integrable equation for any value of the
parameter $\lambda\in \textbf{C}$. For constructing the operator $L_1$ we use
the concept of the invariant manifold which is a generalization of the
symmetry. Then for searching $L_2$ we take an auxiliary linear equation
connected with the linearized equation by the Darboux transformation.
Connection of the invariant manifold with the Lax pairs and the
Dubrovin-Weierstrass equations is discussed.
