An algorithm has been developed to study the nonlinear propagation of high-amplitude jet noise. The hybrid time-frequency domain algorithm employs a split-step solution to a Mendousse-Burgers equation that includes the effects of quadratic nonlinearity, atmospheric absorption and dispersion, and geometrical spreading. Spectral predictions generated using the algorithm are compared to recent F/A-18E engine run-up noise measurements made at afterburner and military thrust conditions at distances of 74 and 150 m from the engine nozzles. The agreement between the predicted and measured spectra is such that the results help confirm that energy transfer is occurring to higher frequencies. However, the differences between the model and the measurement raise important issues regarding some of the physical phenomena likely associated with the measurement but not accounted for in the model. Among these are the substantial multipath interference effects in the measured spectra and the finite extent of the aeroacoustic sources within the jet.