Nonlinear evolution of lower hybrid (LH) waves is studied by means of a fully three-dimensional parallel particle-in-cell (PPIC) code. The plasma is driven by a monochromatic LH pump wave, which drives secondary LH and low-frequency waves having a broad frequency spectrum from &ohgr;⪝&OHgr;i to &ohgr;~&ohgr;o>&ohgr;lh, where &OHgr;i, &ohgr;o and &ohgr;lh are the ion cyclotron, pump and LH resonance frequencies, respectively. The temporal variations in the electric field components show both amplitude and phase modulations. In a plasma with equal electron and ion temperatures the dominant amplitude modulation occurs at the ion cyclotron timescale &tgr;ci. The pondermotive force associated with the vector nonlinearity arising from the E_¿B_ drift of electrons is seen to generate both density depletions and enhancements depending on the time-varying phase difference between the orthogonal electric field components Ex and Ey transverse to the ambient magnetic field B_o in the z direction. Despite the use of quite strong pump wave amplitude, wave collapse in density cavities alone is not seen; instead, equally strong density cavities (cavitons) and enhancements (pilons) occur quasi-periodically both in time and space. The phase difference between Ex and Ey and its evolution yield a rotating transverse electric field vector with hodograms of Ex and Ey changing with time. The temporal evolution of the parallel acceleration of electrons and transverse heating of ions are discussed. For relatively slow pumps the electron acceleration is predominantly unidirectional parallel to the pump phase velocity V_p∥o. On the other hand, for sufficiently large pump phase velocities the acceleration becomes bidirectional. The parallel electron acceleration up to V∥ max~2Vp∥o is common, and the transverse ion acceleration occurs up to V⊥ max≅(m/M)1/2Vp∥o≅Vp⊥o, where m and M are the electron and ion mass, respectively. The relevance of the above results to the observations on LH waves and their role in electron and ion accelerations is discussed. ¿ 1998 American Geophysical Union