Abstract
Water waves are actively studied. A new method to generate new wave sys-tems through making perturbation in matrix spectral problems for integrable couplings is presented, which is called the "completion process of integrable couplings". As its ap-plication, we construct an integrable coupling hierarchy and show that each equation in the resulting hierarchy has a bi-Hamiltonian structure by taking use of the component-trace identity. Moreover, the self-consistent sources of integrable coupling is presented based on the theory of self-consistent sources.