Abstract. In solar wind, dissipation of slow-mode magnetosonic waves may play a significant role in heating the solar wind, and these modes contribute essentially to the solar wind compressible turbulence. Most previous identifications of slow waves utilized the characteristic negative correlation between δ|B| and δρ. However, that criterion does not well identify quasi-parallel slow waves, for which δ|B| is negligible compared to δρ. Here we present a new method of identification, which will be used in 3-D compressible simulation. It is based on two criteria: (1) that V_pB0 (phase speed projected along B₀) is around ± c_s, and that (2) there exists a clear correlation of δv_|| and δρ. Our research demonstrates that if v_A > c_s, slow waves possess correlation between δv_|| and δρ, with δρ / δv_|| ≈ ± ρ₀ / c_s. This method helps us to distinguish slow-mode waves from fast and Alfvén waves, both of which do not have this polarity relation. The criteria are insensitive to the propagation angle θ_{k B}, defined as the angle between wave vector k and B₀; they can be applied with a wide range of β if only v_A > c_s. In our numerical simulation, we have identified four cases of slow wave trains with this method. The slow wave trains seem to deform, probably caused by interaction with other waves; as a result, fast or Alfvén waves may be produced during the interaction and seem to propagate bidirectionally away. Our identification and analysis of the wave trains provide useful methods for investigations of compressible turbulence in the solar wind or in similar environments, and will thus deepen understandings of slow waves in the turbulence.