  We extend the reactive Burgers equation presented in Kasimov et al. Phys.
Rev. Lett., 110 (2013) and Faria et al. SIAM J. Appl. Maths, 74 (2014), to
include multidimensional effects. Furthermore, we explain how the model can be
rationally justified following the ideas of the asymptotic theory developed in
Faria et al. JFM (2015). The proposed model is a forced version of the unsteady
small disturbance transonic flow equations. We show that for physically
reasonable choices of forcing functions, traveling wave solutions akin to
detonation waves exist. It is demonstrated that multidimensional effects play
an important role in the stability and dynamics of the traveling waves.
Numerical simulations indicate that solutions of the model tend to form
multi-dimensional patterns analogous to cells in gaseous detonations.
