In this article we report steady, two-dimensional, inviscid solutions for the near field and far field of a supersonic reactive flow over a variable-double-ramp geometry/The incident shock wave compresses and heats the reactants that will combust after flowing some induction length* Upon reaction, a detonation wave forms and intersects the leading wave at some distance from the ramp surface. In this article, reaction-polar diagrams are developed and the detonation branch solutions are used to investigate the wave interaction processes that may lead to a steady three-wave structure. By considering this formation process new oblique detonation wave stabilization criteria based on the freestream conditions and ramp geometry are provided.