Ultrashort solitons and their control in the regime of event horizons in nonlinear dispersive optical media

Several key concepts for the description of nonlinear pulse propagation in dispersive optical media will be introduced. Among those are envelope models, short-pulse equations, as well as our generalized approach [1]. Effects like limitations for ultrashort optical pulses [2], cusp formation [3], and solitons that mimic event horizons for smaller optical waves will be presented. Moreover, it will be demonstrated, both numerically and more efficiently by a new analytic theory [4], that small optical waves can be used to control such solitons [5], [6].