The KZK equation is the reference equation for the modeling of finite amplitude diffraction effects. It has been applied with success to many applications in various domains. Nevertheless, the parabolic approximation underlying the KZK equation limits the validity of this one to narrow‐angle propagation. A new formulation of the Kuznetsov equation enables us to go beyond the parabolic approximation for the diffraction effects in the homogeneous case, the parabolic approximation being now limited only to the heterogeneous perturbation which is one order of magnitude smaller. This method formalizes and generalizes to the weakly heterogeneous case the previous work of Christopher and Parker [J. Acoust. Soc. Am. 90, 488–499 (1991)]. Special attention is paid to the implementation of boundary conditions (such as absorbing or perfectly matched layers). Several validation tests will illustrate the potential of the method, such as nonlinear focusing or scattering. Applications to sonic boom propagation in a turbulent atmosphere will finally be discussed.