A conjecture concerning nonlocal terms of recursion operators

We provide examples to extend a recent conjecture concerning the relation between zero curvature representations and nonlocal terms of inverse recursion operators to all recursion operators in dimension two. Namely, we conjecture that nonlocal terms of recursion operators are always related to a suitable zero-curvature representation, not necessarily depending on a parameter or taking values in a semisimple algebra. In particular, the conventional pseudodifferential recursion operators correspond to abelian Lie algebras. __________ Translated from Fundamentalnaya i Prikladnaya Matematika (Fundamental and Applied Mathematics), Vol. 12, No. 7, pp. 23–33, 2006.