An Extension of the KdV Hierarchy Arising from a Representation of a Toroidal Lie Algebra
Abstract
Description
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 $sl_2$ - 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.
22 pages, plain tex, no figures
22 pages, plain tex, no figures