Abstract According to observations by the Freja satellite in the upper ionosphere, amplitudes of magnetic disturbances associated with observed density solitons are only several 10 −2 nT or less. These very weak magnetic disturbances can be neglected against the ambient magnetic field of 0.2 Gauss in Freja's orbit region. In this paper we establish an electrostatic model for the nonlinear waves observed on board of Freja. The fluid equations are used and the “Sagdeev potential” is derived to study the nonlinear waves. The results show the existence not only of solitons with a density hump and solitons with a density dip, but also of periodic density waves and density shock waves. The theoretic amplitudes of the solitons may vary between 20% and a factor of 2, which is consistent with the observations on board of Freja. Some waveforms of the solitons with a density dip are very similar to the observed ones.