Hamiltonian structure of an operator valued extension of Super KdV equations
A. Restuccia, A. Sotomayor
TL;DR
This paper extends the super KdV integrable system to operator-valued functions, introduces transformations, and derives its Hamiltonian structure and conserved quantities, broadening understanding of supersymmetric integrable models.
Contribution
It presents a novel operator-valued extension of the super KdV system, including transformations and Hamiltonian structure analysis, with implications for integrable supersymmetric models.
Findings
Extended super KdV system with operator-valued functions
Miura and Gardner transformations for the extended system
Infinite conserved quantities identified
Abstract
An extension of the super Korteweg-de Vries integrable system in terms of operator valued functions is obtained. In particular the extension contains the Super KdV and coupled systems with functions valued on a symplectic space. We introduce a Miura transformation for the extended system and obtain its hamiltonian structure. We also obtain an extended Gardner transformation which allows to find an infinite number of conserved quantities of the extended system.
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