Squared Eigenfunction Symmetries for Soliton Equations: Part II

Abstract

Nonlinear integrable evolution equations in 1+1 dimensions arise from constraints of the 2+1-dimensional hierarchies associated with the Kadomtsev-Petviashvili (KP) equation, the modified KP equation and the Dym equation, respectively. Links of Bäcklund type and of reciprocal type are known to exist between the 2+1-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. © 1998 Academic Press.