The filamentation of an electromagnetic wave in a hot plasma can be described in terms of the nonlinear interaction between the initial plane electromagnetic wave k0, pairs of Stokes and anti-Stokes waves k0-or+ks, and their associated density perturbations ks. The authors have analysed the nonlinear development of this process by considering the evolution of the initial plasma wave and those waves for which the initial growth rate is a maximum. The justification for this approximation comes from a recent theorem of Thyagaraja which enables one to show that for typical experimental conditions there are only a few effective degrees of freedom (or modes) for this interaction. The equation can be solved analytically for a number of special cases. In particular the stationary wave solutions yield a simple expression for the nonlinear filamentation length which is in fair agreement with recent experiments.