A nonlinear time domain counterpart of the linear frequency domain parabolic wave equation (PE) has been derived for investigation of pulse propagation in a refracting medium, including caustics. Assuming nearly unidirectional propagation, equations of hydrodynamics yield a quadratic correction term for the linear second‐order wave equation. Perturbation analysis about unidirectional wave propagation yields a first‐order nonlinear progressive wave equation (NPE) cast in a wave following frame. This equation explicitly separates terms for the physical processes of refraction, nonlinear steepening, radial spreading, and diffraction. Self‐refraction is manifest through a continuous interaction between steepening and diffraction terms. When the wave is taken to be linear and monochromatic, the NPE reduces to the familiar PE, within appropriate assumptions. A new numerical algorithm of the flux correction type has been constructed for integration of the NPE. Successful applications to date include: (1) development of initially smooth pulses into agingNwave shocks, (2) wideband linear pulse propagation in a slab, and (3) the evolution of a nonlinearNwave incident on a caustic. [Work supported by ONR].