An Extension of the KdV Hierarchy Arising from a Representation of a Toroidal Lie Algebra

Details An Extension of the KdV Hierarchy Arising from a Representation of a Toroidal Lie Algebra An Extension of the KdV Hierarchy Arising from a Representation of a Toroidal Lie Algebra

1997-06-18

arxiv.org/abs/solv-int/9706008v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages, plain tex, no figures

Scientific paper

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.

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