Collisionless shock resolution in nematic liquid crystals

The diffractive resolution on a collisionless shock formed along the spatial profile of a beam in a nematic liquid crystal is considered, this material being an example of a self-focusing, nonlocal medium. It is found that the shock is resolved through the formation of an undular bore structure which persists for experimentally relevant propagation distances due to nonlocality delaying the onset of modulational instability. Both 1+1 and 2+1 dimensional bores with circular symmetry are considered (termed line and circular bores, respectively). A semianalytical solution is developed for the line undular bore, approximating it as a train of uniform solitary waves. The predictions of this semianalytical theory are found to be in excellent agreement with numerical solutions of the governing equations, both for line and circular bores. The method presented here yields semianalytical results for a bore in focusing media.