L–A–B representation for nonlinear evolution equations and its applications

In this paper we consider the L–A–B representation of nonlinear evolution equations (NLEEs) and present an approach to determine its range. The method we adopt is that of Lie quotient algebras. As an example, we consider the Kaup–Newell spectral problem and give a category of NLEEs associated with it. Particularly, we obtain the negative order hierarchies of NLEEs by considering the inverse of recursion operator