The non-linear coupling of lower hybrid waves excited by a waveguide array is examined numerically and analytically in a model of a tokamak plasma. The non-linearity considered is the ponderomotive force and the fields are evolved self-consistently in time to the steady state. Simplified coupling models are derived for the loading of large and small arrays and for different phasings of the waveguides. It is found that the reflection coefficient can be modified considerably by the non-linear effects and that the non-linear modification of the power spectrum is especially large when the array excites two resonance cones. The fields filament and the spectrum is broadened and upshifted. The travelling-wave excitation, which excites a single resonance cone and is considered for current drive, is less affected non-linearly; the fields do not filament and the spectrum remains narrow.