Vector NLS hierarchy solitons revisited: dressing transformation and tau function approach

Abstract

We discuss some algebraic aspects of the integrable vector non-linear Schrödinger hierarchies (GNLS${}_r$). These are hierarchies of zero-curvature equations constructed from affine Kac-Moody algebras ${\widehat{sl}}_{r+1}$. Using the dressing transformation method and the tau-function formalism, we construct the N-soliton solutions of the GNLS${}_r$ systems. The explicit matrix elements in the case of GNLS${}_1$ are computed using level one vertex operator representations.

arXiv commentLaTex, 41 pages

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