An Operator Valued Extension of the Super KdV Equations

TL;DR

This paper extends the Super KdV integrable system using operator-valued functions and develops an algebraic method to find infinitely many conserved quantities, generalizing known results.

Contribution

It introduces an operator-valued extension of the Super KdV equations and provides a systematic algebraic approach to derive conserved quantities.

Findings

Constructed infinitely many conserved quantities for the extended system.

Reduced conserved quantities to those of the classical Super KdV in a special case.

Established a general algebraic framework for integrable systems with operator-valued functions.

Abstract

An extension of the Super 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.