Algebraic Aspects of Integrable Systems

Irene Dorfman died in Moscow on April 6, 1994, shortly after seeing her beautiful book on Dirac structures [I]. The present volume contains a collection of papers aiming at celebrating her outstanding contributions to mathematics. Her most important discoveries are associated with the algebraic structures arising in the study of integrable equations. Most of the articles contained in this volume are in the same spirit. Irene, working as a student of Israel Gel'fand made the fundamental dis­ covery that integrability is closely related to the existence of bi-Hamiltonian structures [2], [3]. These structures were discovered independently, and al­ most simultaneously, by Magri [4] (see also [5]). Several papers in this book are based on this remarkable discovery. In particular Fokas, Olver, Rosenau construct large classes on integrable equations using bi-Hamiltonian struc­ tures, Fordy, Harris derive such structures by considering the restriction of isospectral flows to stationary manifolds and Fuchssteiner discusses similar structures in a rather abstract setting.