Group Analysis of Differential Equations and Integrable Systems − 2018

Yves Grandati (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.