Non-local models involving the Hilbert transform are essential for understanding complex interactions in nonlinear systems. In this study, we refine the Ablowitz–Fokas–Kruskal (AFK) method to generate and solve new non-local models. By applying this modified approach to both the linear and bilinear Schrodinger equations, we successfully derive novel non-local models, including the Mikhailov–Novikov equation and a series of non-local nonlinear Schrodinger (NLS) equations. Ouranalysis yields exact rational solutions, revealing distinctive behaviors such as finite time blow-up and complex wave patterns. Furthermore, we confirm the integrability of these models by establishing their Lax pairs. These findings highlight the effectiveness of the modified AFK method in generating and solving non-local models, thereby contributing to a deeper understanding of non-local dynamics and their applications.