An Averaged Lagrangian Method for Dissipative Wavetrains

We modify the averaged Lagrangian method for analysing slowly varying nonlinear wavetrains to include cases with small dissipation. To do this, we use a pseudo-variational principle introduced by Prigogine in which the Lagrangian depends on a function to be varied and the solution of the problem; this can be used to describe irreversible processes. Examples of applications to both ordinary and partial differential equations are presented.