Integrability of Dirac reduced bi-Hamiltonian equations

De Sole, A., Kac, V. G. and Valeri, D. (2014) Integrability of Dirac reduced bi-Hamiltonian equations. In: Anconca, V. and Strickland, E. (eds.) Trends in Contemporary Mathematics. Series: Springer INdAM series (8). Springer: Cham, pp. 13-32. ISBN 9783319052533 (doi: 10.1007/978-3-319-05254-0_2)

Abstract

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.

• Item Type: Book Sections
• Status: Published
• Glasgow Author(s) Enlighten ID: Valeri, Dr Daniele
• Authors: De Sole, A., Kac, V. G., and Valeri, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Publisher: Springer
• ISBN: 9783319052533
• Published Online: 02 August 2014