Squared eigenfunction symmetries for soliton equations. I
[For part II of this paper see the following review Zbl 0896.35118.] This paper is concerned with three classes of soliton systems associated with scalar Lax operators, namely, the \(2+1\)-dimensional hierarchies of the KP equation, the modified KP equation, and the Dym equation. These classes are related to one another by gauge transformations and reciprocal links. For each of these classes the authors give an algebraic construction of the symmetry transformation generated by products of eigenfunctions. They also extend the links among the soliton hierarchies to these symmetries.
scientific article; zbMATH DE number 1115464
scientific article