Abstract
Integrable couplings are associated with non-semisimple Lie algebras. In this paper, we propose a newmethod to generate newintegrable systems through making perturbation in matrix spectral problems for integrable couplings, which is called the "completion process of integrable couplings." As an example, the idea of construction is applied to the Ablowitz-Kaup-Newell-Segur integrable coupling. Each equation in the resulting hierarchy has a bi-Hamiltonian structure furnished by the component-trace identity. Published by AIP Publishing.