An operator valued extension of the super Korteweg–de Vries equations

Abstract

An extension of the super Korteweg–de Vries (KdV) integrable system in terms of operator valued functions is obtained. Following the ideas of Gardner, a general algebraic approach for finding the infinitely many conserved quantities of integrable systems is presented. The approach is applied to the above described system and infinitely many conserved quantities are constructed. In a particular case they reduce to the corresponding conserved quantities of super KdV.