Reducibility of zero curvature representations with application to inverse recursion operators

Abstract:
A zero curvature representation (ZCR) taking values in a solvable subalgebra is equivalent to a chain of conservation laws. A criterion to detect reducibility of a ZCR to a solvable subalgebra will be presented. Given an inverse recursion operator in Guthrie form, results lead to a recipe to express it in terms of D^-1.