A hierarchy of coupled evolution equations with self-consistent sources and the dressing method

Abstract

The dressing method, based on the local 3 × 3 matrix -problem, is used to study the two-coupled integrable nonlinear evolution equations with self-consistent sources. A hierarchy of the nonlinear evolution equations associated with a 3 × 3 matrix problem, including the coupled nonlinear Schrödinger equation and Maxwell–Bloch equation, is derived by introducing a suitable recursion operator. Explicit solutions, including N-soliton solutions, for the hierarchy in a closed form are obtained by virtue of the properties of the Cauchy matrix.