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A novel approach — based upon vertex operator representation — is devised to study the AKNS hierarchy. It is shown that this method reveals the remarkable properties of the AKNS hierarchy in relatively simple, rather natural and particularly effective ways. In addition, the connection of this vertex operator based approach with Lie-algebraic integrability schemes is analyzed and its relationship with τ-function representations is briefly discussed.

The AKNS Hierarchy Revisited: A Vertex Operator Approach and its Lie-Algebraic Structure