  We study spectra of long wavelength plasma oscillations in a system of two
energy splitted one-dimensional (1D) massless Dirac fermion subbands coupled by
spin-orbit interaction. Such a system may be formed by edge subbands in
semiconducting transition metal dichalcogenide monolayers. Intrasubband
transitions of massless Dirac fermions give rise to optical and acoustic
gapless branches of intrasubband 1D plasmons. We reveal that the optical branch
is of quantum character with group velocity being inverse proportional to
square root of the Planck constant, whereas the acoustic branch is classical
one with group velocity proportional to geometric mean of the edge subband
velocities. Spin-orbit interaction, allowing intersubband transitions in the
system, results in emergence of two branches of intersubband 1D plasmons: upper
and lower ones. The upper and lower branches are gapped at small wave vectors
and evolve with positive and negative group velocities, respectively, from
energy splitting of the edge subbands at Fermi-level. The both intersubband
branches adjoin intersubband single particle excitation continuum from above,
while in case of the edge subbands with unequal velocities the lower one
experiences Landau damping at small wave vectors. In addition, the lower
branch, attaining zero frequency at a non-zero wave vector, alters its group
velocity from negative to positive one.
