Recent experimental work has demonstrated optical control of spin wave emission by tuning the shape of the optical pulse (Satoh et al. Nature Photonics, 6, 662 (2012)). We reproduce these results and extend the scope of the control by investigating nonlinear effects for large amplitude excitations. We observe an accumulation of spin wave power at the center of the initial excitation combined with short-wavelength spin waves. These kind of nonlinear effects have not been observed in earlier work on nonlinearities of spin waves. Our observations pave the way for the manipulation of magnetic structures at a smaller scale than the beam focus, for instance in devices with all-optical control of magnetism.