Squared Eigenfunction Symmetries for Soliton Equations: Part I

Three classes of soliton systems associated with scalar Lax operators are considered. They represent, in turn, the 2q1-dimensional hierarchies of the KP equation, the modified KP equation and the Dym equation. They are related via gauge transformations and reciprocal links. For each class an algebraic construction of the symmetry transformation generated by products of adjoint.eigenfunctions is given. The links between the soliton hierarchies are extended to these symmetries