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

Harold Blas

paper

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

arXiv:solv-int/9912015

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 $s l^_{r + 1}$ . 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.

LaTex, 41 pages