Coupled Nonlinear Schrödinger Equations and the Miura Transformation

A wide class of coupled nonlinear Schrödinger (NLS) equations are derived by virtue of the dressing method, and the associated parametric solutions are discussed. As an illustration, the explicit solution of the coupled NLS-type equation associated with σ₁ is given. The Miura transformation for a AKNS-type hierarchy is established, from which a modified coupled NLS-type equation is shown to be equivalent to the Heisenberg spin equation.