Collisionless shock resolution in nematic liquid crystals
G. Assanto, T. Marchant and N. Smyth
Phys. Rev. A 78 (6), 063808 (2009)
Abstract:The diffractive resolution on a collisionless shock formed along the spatial profile of a beam in nematic liquid crystals 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 modulation instability. Both 1+1 and 2+1 dimensional bores with circular symmetry are considered (termed line and circular bores, respectively). A semi-analytical solution is developed for the line undular bore, approximating it as a train of uniform soitary waves. The predictions of this semi-analytical theaory are found to be in excellent agreement with numerical solutions of the governing equations, both for line and circular bores. The method presented hereby is a novel technique yielding semi-analytical results for a bore in focusing media.