# Integrability of Dirac reduced bi-Hamiltonian equations

@article{Sole2014IntegrabilityOD,
title={Integrability of Dirac reduced bi-Hamiltonian equations},
author={Alberto De Sole and Victor G. Kac and Daniele Valeri},
journal={arXiv: Mathematical Physics},
year={2014},
pages={13-32}
}
• Published 23 January 2014
• Mathematics
• arXiv: Mathematical Physics
First, we give a brief review of the theory of the Lenard-Magri scheme for a non-local bi-Poisson structure and of the theory of Dirac reduction. These theories are used in the remainder of the paper to prove integrability of three hierarchies of bi-Hamiltonian PDE’s, obtained by Dirac reduction from some generalized Drinfeld-Sokolov hierarchies.
6 Citations
These lectures were given in Session 1: “Vertex algebras, W-algebras, and applications” of INdAM Intensive research period “Perspectives in Lie Theory” at the Centro di Ricerca Matematica Ennio De
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In our previous work we studied minimal fractional decompositions of a rational matrix pseudodifferential operator: H=A/B, where A and B are matrix differential operators, and B is non-degenerate of
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The skewfield $$\mathcal{K }(\partial )$$K(∂) of rational pseudodifferential operators over a differential field $$\mathcal{K }$$K is the skewfield of fractions of the algebra of differential