An extension of the Korteweg-de Vries hierarchy arising from a representation of a toroidal Lie algebra

Abstract

In this article we show how to construct hierarchies of partial differential equations from the vertex operator representations of toroidal Lie algebras. In the smallest example - rank 2 toroidal cover of sl2 - we obtain an extension of the KdV hierarchy. We use the action of the corresponding infinite-dimensional group to construct solutions for these non-linear PDEs. © 1999 Academic Press.