In this work, we study time evolution equations of null curves according to acceleration vector fields in Minkowski 3-space. First of all, we find a solution of the nonlinear system of time evolution equations for planar null curves. Also, we introduce a null binormal acceleration (NBA) flow ∂2γ/∂t2 = κe3 along a null curve γ. From this, we study soliton solutions of the NBA flow in Minkowski plane. Also, we give some soliton solutions of the NBA flows by using d’Alembert partial differential equation in Minkowski 3-space. Lastly, we construct Bäcklund transformations corresponding to the NBA flows, and we study soliton solutions of integrable system in the intrinsic invariants of the null curve by using hyperbolic functions.