Nonlinear dispersive oscillatory waves are analyzed for Korteweg‐deVries type partial differential equations with slowly varying coefficients and arbitrary small perturbations. Spatial and temporal evolution of the amplitude parameters are determined in the usual way by the possible dissipation of the wave actions for both momentum and energy. For dissipative perturbations, both wave actions are shown to be valid to a higher order. Thus, the first variation of the wave action equations is used to derive equations for the slow modulations of the phase shift. It is shown that the phase shift satisfies a set of two coupled linear equation