  We prove the existence of the modified wave operators for a scalar
quasilinear wave equation satisfying the weak null condition. This is
accomplished in three steps. First, we derive a new reduced asymptotic system
for the quasilinear wave equation by modifying H\"{o}rmander's method. Next, we
construct an approximate solution, by solving our new reduced system given some
scattering data at infinite time. Finally, we prove that the quasilinear wave
equation has a global solution which agrees with the approximate solution at
infinite time.
