  We propose a theory of weakly nonlinear multi-dimensional self sustained
detonations based on asymptotic analysis of the reactive compressible
Navier-Stokes equations. We show that these equations can be reduced to a model
consisting of a forced, unsteady, small disturbance, transonic equation and a
rate equation for the heat release. In one spatial dimension, the model
simplifies to a forced Burgers equation. Through analysis, numerical
calculations and comparison with the reactive Euler equations, the model is
demonstrated to capture such essential dynamical characteristics of detonations
as the steady-state structure, the linear stability spectrum, the
period-doubling sequence of bifurcations and chaos in one-dimensional
detonations and cellular structures in multi- dimensional detonations.
