Reducibility of zero curvature representations with application to recursion operators

by M. Marvan

Preprints: GA 3/2003 and DIPS 03/2003 and nlin.SI/0306006

We present a criterion of reducibility of a zero curvature representation to a solvable subalgebra, hence to a chain of conservation laws. Namely, we show that reducibility is equivalent to the existence of a section of the generalized Riccati covering. Results are applied to conversion between Guthrie's and Olver's form of recursion operators.