  Recently Mendonca and Cardoso [Phys. Rev. D, vol. 66, 104009 (2002)]
considered nonlinear gravitational wave packets propagating in flat space-time.
They concluded that the evolution equation - to third order in amplitude -
takes a similar form to what arises in nonlinear optics. Based on this
equation, the authors found that nonlinear gravitational waves exhibit
self-phase modulation and high harmonic generation leading to frequency
up-shifting and spectral energy dilution of the gravitational wave energy. In
this Brief Report we point out the fact - a possibility that seems to have been
overlooked by Mendonca and Cardoso - that the nonlinear terms in the evolution
equation cancels and, hence, that there is no amplitude evolution of the pulse.
Finally we discuss scenarios where these nonlinearities may play a role.
