In this paper, we derive a new negative order generalized Ablowitz-Kaup-Newell-Segur system associated with a \(4 \times 4\) matrix spectral problem. The infinitely many conservation laws and Hamiltonian structures of this system are constructed. The Darboux transformation of the negative order generalized Ablowitz-Kaup-Newell-Segur system is established and some multi-soliton solutions expressed by quasi-determinants are given. It is remarkable that two-solitons exhibit scattering with both phase shifts and amplitude changes. As a reduction, the Darboux transformation of two reduced systems and their soliton solutions including single-hump and double-hump solitons are obtained.
