On an equation of the Drinfeld-Sokolov hierarchy

R. Conte (1, 2)

1 ENS Paris Saclay - Ecole Normale Supérieure Paris-Saclay
2 Department of Mathematics, The University of Hong Kong

A seventh order ordinary differential equation (ODE) arising by reduction of the Drinfeld-Sokolov hierarchy is shown to be identical to a similarity reduction of an equation in the hierarchy of Sawada-Kotera. We also exhibit its link with a particular F-VI, a fourth order ODE isolated by Cosgrove which is likely to define a higher order Painlev\'e function.

Mots clés: Drinfeld-Sokolov hierarchy; higher Painlevé equation

Domaines: Science non linéaire [physics]

R. Conte. On an equation of the Drinfeld-Sokolov hierarchy. Open Communications in Nonlinear Mathematical Physics, 2024. ⟨hal-04549364⟩