In solar wind,slow mode magnetosonic waves are scarce to be identified,but their dissipation plays one of key roles in heating the solar wind,and the wave mode contributes essentially to the solar wind compressible turbulence.Most previous identifications of slow waves utilized negative correlation between δ |B| and δρ.That criterion does not well identify quasi-parallel slow waves,for which δ |B| is negligible compared to δρ.Herewith we present a new method 5 of identification,which will be used in 3D compressible simulation,based on two criteria: (1) VpB0 (phase speed projected along B0) is around ±cs; (2) there exists correlation of δvk and δρ.Our research demonstrates that if vA > cs,slow waves possess good correlation of δvk and δρ,with δρ/δvk ≈ ±ρ0/cs.This method helps us to distinguish slow mode waves from fast / Alfv′en waves,both of which do not have this polarity relation.The criteria are insensitive to the propagation angle θkB,defined as the angle between wave vector k and B0.In our numerical simulation,we have identified four cases of slow wave trains with this method.Our cases explain observations of slow waves in the solar wind,especially in compressibility Cp and dimensionless cross helicity σc.The slow wave trains seem to deform,probably caused by interaction with other waves; as a result,fast or Alfv′en waves may be produced during the interaction and propagate bidirectionally away from the mode conversion site.Our identification and analysis of the wave trains will provide possible methods for investigations of compressible turbulence in the solar wind or in similar environments and deepen understandings of slow waves in the turbulence.