  We present the first attempt to analytically study the nonlinear matter power
spectrum for a mixed dark matter (cold dark matter plus neutrinos of total mass
~0.1eV) model based on cosmological perturbation theory. The suppression in the
power spectrum amplitudes due to massive neutrinos is, compared to the linear
regime, enhanced in the weakly nonlinear regime where standard linear theory
ceases to be accurate. We demonstrate that, thanks to this enhanced effect and
the gain in the range of wavenumbers to which the PT prediction is applicable,
the use of such a nonlinear model may enable a precision of sigma(m_nu,tot) ~
0.07eV in constraining the total neutrino mass for the planned galaxy redshift
survey, a factor of 2 improvement compared to the linear regime.
