2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71646In this paper we construct a family of commuting multidimensional differential operators of order 3, which is closely related to the KdV hierarchy. We find a common eigenfunction of this family and an algebraic relation between these operators. Using these operators we associate a hyperelliptic curve to any solution of the stationary KdV equation. A basic generating function of the solutions of stationary KdV equation is introduced as a special polarization of the equation of the hyperelliptic curve. We also define and discuss the notion of a $w$-function of a solution of the stationary $g$-KdV equation.Dynamical Systemstext