Theory of weakly nonlinear self sustained detonations

We derive a new weakly non-linear asymptotic model of detonation waves capable of capturing the rich dynamics observed in solutions of the reactive Euler equations, both in one and multiple space dimensions. We then investigate the travelling wave solutions of the asymptotic model, together with their linear stability. Finally, we study the non-linear dynamics through numerical simulations, and present a quantitative comparison between the asymptotic equations and the full system they are expected to approximate.