A solution to the ultrarelativistic strong explosion problem with a nonpower law density gradient is delineated. We consider a blast wave expanding into a density profile falling off as a steep radial power law with small, spherically symmetric, and log-periodic density perturbations. We find discretely self-similar solutions to the perturbation equations and compare them to numerical simulations. These results are then generalized to encompass small spherically symmetric perturbations with arbitrary profiles.
Bibliographical noteFunding Information:
The authors wish to thank Professor Tsvi Piran for fruitful discussions. This research was partially supported by a NASA grant, IRG grant, and a Packard Fellowship.