Hamiltonian structure of an operator valued extension of Super KdV equations


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.Comment: Contribution to the Proceedings of the XXIst International Conference on Integrable Systems and Quantum Symmetries(ISQS21)(June 11-16, 2013, Prague, Czech Republic), 6 page

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