Hamiltonian structure of an operator valued extension of Super KdV equations

21st International Conference on Integrable Systems and Quantum Symmetries

Restuccia, Alvaro^1,2 ; Sotomayor, Adrián^3

Physics Department, Universidad de Antofagasta, Antofagasta, Chile^1

Physics Department, Universidad Simón Bolívar, Caracas, Venezuela^2

Departament of Matemathics, Universidad de Antofagasta, Antofagasta, Chile^3

关键词: Conserved quantity;    Extended systems;    Hamiltonian structures;    Integrable systems;    Korteweg-de Vries;    Miura transformations;    Operator-valued functions;    Symplectic spaces;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/474/1/012028/pdf
DOI  :  10.1088/1742-6596/474/1/012028

来源: IOP

【 摘 要 】

An extension of the super Korteweg-de Vries integrable system in terms of operator valued functions is obtained. In particular the extension contains the N = 1 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.