Squared Eigenfunction Symmetries for Soliton Equations: Part I

Abstract

Three classes of soliton systems associated with scalar Lax operators are considered. They represent, in turn, the 2 q 1-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 Ž . the symmetry transformation generated by products of adjoint eigenfunctions is given. The links between the soliton hierarchies are extended to these symmetries.

Matrix generalizations of integrable systems with Lax integro-differential representations

“…Our aim was to generalize Lax representations of the (2+1)-dimensional k-cKP hierarchy to the case of two integro-differential operators, in order to obtain Lax representations for matrix generalizations of Davey-Stewartson systems DS-I, DS-II, DS-III, and their higher order counterparts. We also present a Lax representation, with two integro-differential operators, for a (2+1)-dimensional generalization of the Chen-Lee-Liu equation, which has been obtained in [28].…”

Bäcklund Transformations and Non-Abelian Nonlinear Evolution Equations: a Novel Bäcklund Chart

“…• The approach can be extended also when nonlinear evolution equations in (2 + 1) dimensions are considered, namely, the unknown function is supposed to depend on two space variables rather than on a single space variable. Thus, in [40], the Kadomtsev-Petviashvili (KP), modified Kadomtsev-Petviashvili (mKP) and (…”

Additional Reductions in the K -Constrained Modified KP Hierarchy

“…In [19,20], a k-constrained modified KP (k-cmKP) hierarchy was introduced and investigated. Dressing methods for k-cmKP hierarchy under additional D-Hermitian reductions were also investigated in [21,22].…”