## Abstract

We propose the following model equation, u_{t}+1/2(u2-uu _{s})_{x}=f(x,u_{s}) that predicts chaotic shock waves, similar to those in detonations in chemically reacting mixtures. The equation is given on the half line, x<0, and the shock is located at x=0 for any t≥0. Here, u_{s}(t) is the shock state and the source term f is taken to mimic the chemical energy release in detonations. This equation retains the essential physics needed to reproduce many properties of detonations in gaseous reactive mixtures: steady traveling wave solutions, instability of such solutions, and the onset of chaos. Our model is the first (to our knowledge) to describe chaos in shock waves by a scalar first-order partial differential equation. The chaos arises in the equation thanks to an interplay between the nonlinearity of the inviscid Burgers equation and a novel forcing term that is nonlocal in nature and has deep physical roots in reactive Euler equations.

Original language | English |
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Article number | 104104 |

Journal | Physical Review Letters |

Volume | 110 |

Issue number | 10 |

DOIs | |

Publication status | Published - 8 Mar 2013 |

Externally published | Yes |