Polynomial dynamical systems associated with the KdV hierarchy

Abstract

In 1974, S.P. Novikov introduced the stationary n-equations of the Korteweg–de Vries hierarchy, namely the n-Novikov equations. These are associated with integrable polynomial dynamical systems, with polynomial 2n integrals, in ℂ3n. In this paper, we construct an infinite-dimensional polynomial dynamical system that is universal for all dynamical systems corresponding to the n-Novikov equations. Thus, we solve the well-known problem of the relationship between the n-Novikov equations for different n.

Keywords

• Korteweg–de Vries hierarchy
• n-Novikov equations
• Integrable polynomial dynamical systems