Completion of the Guo-Hierarchy Integrable Coupling with Self-Consistent Sources in a Nonlinear Wave System

. Water waves are actively studied. A new method to generate new wave systems 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.