  The band structure of a quantum wire with the Rashba spin-orbit coupling
develops a pseudogap in the presence of a magnetic field along the wire. In
such a system spin mixing at the Fermi wavevectors $-k_F$ and $k_F$ can be
different. We have investigated theoretically the collective mode of this
system, and found that the velocity of this collective excitation depends
sensitively on the strength of the Rashba spin-orbit interaction and magnetic
field. Our result suggests that the strength of the spin-orbit interaction can
be determined from the measurement of the velocity.
