tokens: are due to bending and breathing modes that might have been caused from the impact of Sagittarius dwarf falling into our Galactic disc (Gómez et al. 2013 ; D'Onghia et al. 2016 , Carrillo et al. 2019 ). Further Gómez et al. ( 2017 ) have shown that bending and breathing modes must be a common feature in most disc galaxies. 6.3 De-projection of corrugations seen in edge-on galaxies Simulations (Edelsohn Elmegreen 1997 ; Gómez et al. 2013 ) show that the bending waves generated by a Sagittarius-like perturber has both radial and azimuthal dependence. So far corrugations in other galaxies have all been detected in edge-on discs (all galaxies in Table 1 except Milky Way) where we see the combined effect of radial and azimuthal dependence. Looking for corrugations in less inclined discs is not an option, unless we look in the velocity space (Alfaro et al. 2001 ; Sánchez-Gil, Alfaro Pérez 2015 ). However, Kamphuis et al. ( 2013 ) combine the HALOGAS data with non-axisymmetric modelling (using a version of TIRIFIC) and deproject H i observations of edge-on galaxy NGC 5023. They find that their data are best explained by an edge-on disc showing radial corrugations (see their fig 10). Hence we stress the importance of non-axisymmetric modelling here as the need of the hour because, with the availability of high-resolution H i data on scores of nearby edge-on galaxies, a statistical study of corrugations is only a small step away. 7 CONCLUSION This study has focused mainly on characterizing corrugations in the dust lanes of a sample of five edge-on galaxies and understanding their physical state. Partial dust waves are seen in many galaxies but only a handful of galaxies show waves long enough to be characterized. This paper is one of the first attempts to give a quantitative estimate of their size and scale as well as address the issue of whether they are stable. In order to strengthen our analyses, we have added four more galaxies including the Milky Way where corrugations have been previously measured in stellar and gaseous discs. The fact that corrugations are seen in stars, gas and dust leads to the possibility of gravitational instability as the likely origin. In fact, five of the nine galaxies that we have tabulated are visibly perturbed (bar/tidal interaction). Our main conclusions from this work are the following: We present the first systematic study of dust corrugations in edge-on galaxies and characterize them by measuring their wavelengths and amplitudes. The amplitude of corrugation seems to depend on the host galaxy mass. The wavelength of corrugation does not show any dependence on host galaxy mass. It is roughly about the stellar disc scale length for most of our sample. By carrying out a stability analysis, we show that the corrugations with wavelengths larger than the scale length of the stellar disc, are stable. We find indications that corrugations can be as common as warps. We also find mounting evidence that corrugations play a
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