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 2 + 1-dimensional hierarc hies 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 g enerated by products of (adjoint) eigenfunctions is given. The links b etween the soliton hierarchies are extended to these symmetries. (C) 1 998 Academic Press.