Abstract
A novel integrable asymmetric coupling of the Ablowitz-Kaup-Newell-Segur (AKNS) system was generated by the completion process of the integrable coupling. We proved the Liouville integrability of the AKNS integrable coupling by deriving its bi-Hamiltonian structures applying the variational identity. Nextly, we investigated the generalized symmetry and infinitely many conservation laws by Hereman method for the integrable coupling system considered in this paper. Finally, we presented the explicit solutions of the resulting integrable coupling system by constructing Darboux transformation for the first time.
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