A family of mappings from the solution spaces of certain generalized Drinfeld-Sokolov
hierarchies to the self-dual Yang-Mills system on R2,2
is described. This provides an
extension of the well-known relationship between self-dual connections and integrable
hierarchies of AKNS and Drinfeld-Sokolov...
Three nonequivalent real forms of the complex twisted N=2 supersymmetric Toda
chain hierarchy (solv-int/9907021) in real N=1 superspace are presented. It is demostrated that they possess a global twisted N=2 supersymmetry. We discuss a new
superfield basis in which the supersymmetry transformations...
Quadratic systems generated using Yang-Baxter equations are integrable in a sense,
but we display a deterioration in the possession of the Painlevé property as the number
of equations in each `integrable system' increases. Certain intermediate systems are
constructed and also tested for the Painlevé...
We describe constructing solutions of the field equations of Chern-Simons and toplogical BF theories in terms of deformation theory of locally constant (flat) bundles.
Maps of flat connections into one another (dressing transformations) are considered. A
method of calculating (nonlocal) dressing symmetries...
Multicomponent KdV-systems are defined in terms of a set of structure constants
and, as shown by Svinolupov, if these define a Jordan algebra the corresponding
equations may be said to be integrable, at least in the sense of having higher-order
symmetries, recursion operators and hierarchies of conservation...
We apply the Darboux theory of integrability to polynomial ODE's of dimension 3.
Using this theory and computer algebra, we study the existence of first integrals for the
3dimensional LotkaVolterra systems with polynomial invariant algebraic solutions
linear and quadratic and determine numerous...