Abstract
Whitham's linear theory of traffic flows is extended to include dispersion and nonlinearity so as to describe the density waves in two-phase flows. An improved multiple-scale expansion incorporating the idea of the Pad\'e approximation is introduced in order to include systematically the higher order dispersion and nonlinearity into the approximate equations. As a result, generic nonlinear evolution equations with nonconservative terms of a form such as ${\ensuremath{\partial}}_{T}{\ensuremath{\partial}}_{X}\ensuremath{\Psi}$ are obtained. It is shown, numerically and analytically, that these terms effectively incorporate not only linear dispersion relation but also some higher order nonlinearity, which we call ``baseline effect.'' This effect is thought to be essential to the density waves in two-phase flows.
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