  We present the first results on the saturation of the f-mode instability in
neutron stars, due to nonlinear mode coupling. Emission of gravitational waves
drives the f-mode (fundamental mode) unstable in fast-rotating, newborn neutron
stars. The initial growth phase of the mode is followed by its saturation,
because of energy leaking to other modes of the star. The saturation point
determines the strain of the generated gravitational-wave signal, which can
then be used to extract information about the neutron star equation of state.
The parent (unstable) mode couples via parametric resonances with pairs of
daughter modes, with the triplets' evolution exhibiting a rich variety of
behaviors. We study both supernova- and merger-derived neutron stars, simply
modeled as polytropes in a Newtonian context, and show that the parent may
couple to many different daughter pairs during the star's evolution through the
instability window, with the saturation amplitude changing by orders of
magnitude.
