  We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully
degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson
equation and the multiple scale expansion technique, a modified nonlocal
nonlinear Schr{\"{o}}dinger (NLS) equation is derived which governs the
evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in
the NLS equation appears due to the group velocity and multi-plasmon
resonances, i.e., resonances induced by the simultaneous particle absorption of
multiple wave quanta. We focus on the regime where the resonant velocity of
electrons is larger than the Fermi velocity and thereby the linear Landau
damping is forbidden. As a result, the nonlinear wave-particle resonances due
to the group velocity and multi-plasmon processes are the dominant mechanisms
for wave-particle interaction. It is found that in contrast to classical or
semiclassical plasmas, the group velocity resonance does not necessarily give
rise the wave damping in the strong quantum regime where $ \hbar k\sim mv_{F}$
with $\hbar$ denoting the reduced Planck's constant, $m$ the electron mass and
$v_F$ the Fermi velocity, however, the three-plasmon process plays a dominant
role in the nonlinear Landau damping of wave envelopes. In this regime, the
decay rate of the wave amplitude is also found to be higher compared to that in
the modest quantum regime where the multi-plasmon effects are forbidden.
