The first theoretical results are reported predicting {\em moving} solitons
residing inside ({\it 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. The moving embedded solitons (ESs)
are doubly isolated (of codimension 2), but, nevertheless, structurally stable.
Like quiescent ESs, moving ESs are argued to be stable to linear approximation,
and {\it semi}-stable nonlinearly. Estimates show that moving ESs may be
experimentally observed as ∼10 fs pulses with velocity ≤1/10th that
of light.Comment: 9 pages 2 figure
