Context. The cusp-core discrepancy is one of the major problems in astrophysics. It results from comparing the observed mass distribution of galaxies with the predictions of Cold Dark Matter simulations. The latter predict a cuspy density profile in the inner parts of galaxies, whereas observations of dwarf and low surface brightness galaxies show a constant density core. Aims. We want to determine the shape of the dark matter potential in the nuclear regions of a sample of six nearby irregular dwarf galaxies. Methods. In order to quantify the amount of non-circular motions which could potentially affect a mass decomposition, we first perform a harmonic decomposition of the HI Hermite velocity fields of all sample galaxies. We then decompose the HI rotation curves into different mass components by fitting NFW and pseudo-isothermal halo models to the HI rotation curves using a chi^2 minimisation. We model the minimum-disc, the minimum-disc+gas, and the maximum-disc cases. Results. The non-circular motions are in all cases studied here of the order of only a few km/s (generally corresponding to less than 25% of the local rotation velocity), which means that they do not significantly affect the rotation curves. The observed rotation curves can better be described by the cored pseudo-isothermal halo than by the NFW halo. The slopes of the dark matter density profiles confirm this result and are in good agreement with previous studies. The quality of the fits can often be improved when including the baryons, which suggests that they contribute significantly to the inner part of the density profile of dwarf galaxies.
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