New Integrable Hierarchies from Vertex Operator Representations of Polynomial Lie Algebras

Details New Integrable Hierarchies from Vertex Operator Representations of Polynomial Lie Algebras New Integrable Hierarchies from Vertex Operator Representations of Polynomial Lie Algebras

2004-05-17

arxiv.org/abs/nlin/0405040v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

50 pages, no figures

Scientific paper

We give a representation--theoretic interpretation of recent discovered
coupled soliton equations using vertex operators construction of affinization
of not simple but quadratic Lie algebras. In this setup we are able to obtain
new integrable hierarchies coupled to each Drinfeld--Sokolov of $A$, $B$, $C$,
$D$ hierarchies and to construct their soliton solutions.

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