  We derive approximate expressions for the dispersion relation of the
nonlinear Klein-Gordon equation in the case of strong nonlinearities using a
method based on the Linear Delta Expansion. All the results obtained in this
article are fully analytical, never involve the use of special functions, and
can be used to obtain systematic approximations to the exact results to any
desired degree of accuracy. We compare our findings with similar results in the
literature and show that our approach leads to better and simpler results.
