In recent years, advancements in technology and precision have brought ultrafast dynamics into greater focus. These techniques, particularly ultrafast probes, enable the measurement of magnetic dynamics in different materials. As a relatively young field, ultrafast magnetism presents many open questions in out-of-equilibrium magnetic systems, such as how electron and magnetic degrees of freedom interact, or how the spin sub-system undergoes thermalization. To address these questions, we study the 2D antiferromagnetic Heisenberg model beyond linear spin-wave theory, aiming to deepen our understanding of magnon-magnon interactions. To visualize and analyze the real-time dynamics of these interactions within the 2D magnetic Brillouin Zone, we implement the corresponding Boltzmann equation.