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+k_s, and their associated density perturbations k_s. 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.