A new set of coupled integro-differential nonlinear lower hybrid (LH) wave equations is derived within the framework of a kinetic theory coupled to the Maxwell equations to study the parametric instabilities (PIs) produced by LH waves in collisional tokamak plasma. Previous models of nonlinear LH wave equations have been significantly improved. The wave equations derived overcome the limits and incorrectness of the standard theory of the PI in inhomogeneous plasma. They allow us to treat the full spectrum in the parallel and poloidal wavenumber of the coupled LH power wave, diffraction effects and possible cascade phenomena, which are elements of the nonlinear LH physics ignored in the standard PI theory. Numerical solutions of the new nonlinear LH wave equations are proposed. The relevant LH frequency spectra produced by PI are calculated, exhibiting characteristic features of PI observed in LH experiments. It is shown that the LH sideband amplification can be overestimated by orders of magnitude by the standard theory of PI. A benchmark of the new model is provided for spatially homogeneous plasmas. The role of the collisions for PI has been assessed. We demonstrate that previous analyses significantly overestimated their stabilization effect.