Squared Eigenfunction Symmetries for Soliton Equations: Part II

Nonlinear integrable evolution equations in 1q1 dimensions arise from constraints of the 2q1-dimensional hierarchies associated with the Kadomtsev] Petviashvili KP. equation, the modified KP equation and the Dym equation, respectively. Links of B¨acklund type and of reciprocal type are known to exist between the 2q1-dimensional systems. The corresponding links between the constrained flows are discussed in a general framework. In particular, squared eigenfunction symmetries generated by solutions of the associated linear scattering problems are considered. The links between the soliton hierarchies are extended to these symmetries.