A conjecture concerning nonlocal terms of recursion operators
Abstract:
We provide examples to extend a recent conjecture concerning 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.