We present a computational study of the parametric excitation of spin waves in thin film disks with a mode-resolved approach. The method involves projecting out the time-dependent magnetization, computed using micromagnetics simulations, onto the spatial profile of the eigenmodes that are obtained from the linearization of the equations of motion. Unlike spectral analysis in the frequency domain, the projection allows for the analysis of transient mode dynamics under parametric excitation. We apply this method to parallel pumping of quantized spin wave modes in in-plane magnetized thin-film disks, where phenomena such as frequency pulling, mutual phase locking, and higher-order magnon scattering processes are identified.

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