Moving embedded solitons

Abstract

The first theoretical results are reported predicting moving isolated solitons residing inside (embedded into) the continuous spectrum of radiation modes. The model taken is a Bragg-grating medium with Kerr nonlinearity and additional second derivative (wave) terms. In parameter space, moving embedded solitons (ESs) are doubly isolated (codimension 2). Unlike the quiescent branches, moving ES existence depends sensitively on the ratio of self/cross-phase modulation, with only one solution occuring at the physical value sigma=1/2. Like quiescent ESs, moving ESs are argued to be stable to linear approximation, and {\it semi}-stable nonlinearly. This tri-stable configuration (static, left and right-travelling) has potential for optical storage of information. Estimates suggest moving ESs may be experimentally observed as approximately 10 fs pulses with velocity up to 1/10th that of light