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

Yuly Billig

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

Yuly Billig

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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 $sl_2$ - 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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Yuly Billig. 1997-06-18. An Extension of the KdV Hierarchy Arising from a Representation of a Toroidal Lie Algebra. https://arxiv.org/abs/solv-int/9706008

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