Self-modulation effects can become important for the propagation of lower hybrid waves in plasma, particularly for the high power levels envisioned in r.f. heating schemes. Earlier studies in two dimensions (in the plane defined by the electric field of the pump wave and the background magnetic field) have led to non-linear propagation equations, such as the MKdV or the non-linear Schrödinger equation, which admit multiple-soliton solutions. These could physically manifest themselves by breaking up the resonance cones into filaments with intense localized electric fields and could further lead to localized heating. This problem is studied in three dimensions with the motivation of including two additional physical factors. First, the non-linear effect arising from the motion of electrons is included; this leads to an enhancement in the threshold value for the formation of solitons. Secondly, the stability of the two-dimensional solitons to perturbations in the third dimension is studied, and it is found that the third dimension introduces additional dispersive effects which render the solitons unstable to these perturbations.