2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/94564We 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 $\hat{sl}_{r+1}$. 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.LaTex, 41 pagesExactly Solvable and Integrable SystemsHigh Energy Physics - TheoryMathematical Physicstext