Group Analysis of Differential Equations and Integrable Systems − 2018
(Laboratoire de Physique et Chimie Théoriques, Université de Lorraine, Metz, France)
Rational solutions of PIV and PV hierarchies
We present a new approach to determine in a direct and explicit way all the rational solutions of
the dressing chains of odd period (PIV hierarchy). The method is enlarged to dressing chains of even
period (PV hierarchy) generating sets of rational solutions labelled by specific universal characters.
We conjecture they cover all the rational solutions of these higher PV equations.